To show that P(X=0) = e − λ

Question

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Answer 1

Question

Chapter 6.3, Problem 29E

a)

To determine

To show that P(X=0) = e−λ

a)

Expert Solution

Answer to Problem 29E

P(X=0) = e−λ

Explanation of Solution

Given:

X be the event that occurs in a 1-second interval.

Calculation:

Let, Probability mass function of Poisson distribution is,

P(X=x)=e−λλxx!

Therefore, just put x =0 in above formula,

P(X=0)=e−λλ00!=e−λ

b)

To determine

To explain why X=0 is same as T>1

b)

Expert Solution

Answer to Problem 29E

X=0 is same as T>1

Explanation of Solution

Given:

X be the event that occurs in a 1-second interval.

Calculation:

Here, X=0 mean there are no events occurred in 1 second. That is, the amount of time that elapses until the next event will be greater than 1.

That’s why X=0 is same as T>1.

c)

To determine

To show that P(X=0) is same as P(T>1)

c)

Expert Solution

Answer to Problem 29E

P(X=0)= P(T>1)

Explanation of Solution

Given:

X be the event that occurs in a 1-second interval.

Calculation:

Here, X=0 mean there are no events occurred in 1 second. That is, the amount of time that elapses until the next event will be greater than 1.

Therefore, P(X=0) = e−λ

And P(T>1)= e−λ

Both are same.

d)

To determine

To show that P(X=0) = e−2λ for 2-second interval.

d)

Expert Solution

Answer to Problem 29E

P(X=0) = e−2λ

Explanation of Solution

Given:

X be the event that occurs in a 2-second interval.

Calculation:

Let, Probability mass function of Poisson distribution is,

P(X=x)=e−2λ(2λ)xx!=e−2λ

Therefore, just put x =0 in above formula,

P(X=0)=e−2λ(2λ)00!=e−2λ

e)

To determine

To explain why X=0 is same as T>2

e)

Expert Solution

Answer to Problem 29E

X=0 is same as T>2

Explanation of Solution

Given:

X be the event that occurs in a 2-second interval.

Calculation:

Here, X=0 mean there are no events occurred in 2 second. That is, the amount of time that elapses until the next event will be greater than 2.

That’s why X=0 is same as T>2.

f)

To determine

To show that P(X=0) = e−tλ for t-second interval.

f)

Expert Solution

Answer to Problem 29E

P(X=0) = e−tλ

Explanation of Solution

Given:

X be the event that occurs in a t-second interval.

Calculation:

Let, Probability mass function of Poisson distribution is,

P(X=x)=e−tλ(tλ)xx!=e−tλ

Therefore, just put x=0 in above formula,

P(X=0)=e−tλ(tλ)00!=e−tλ

g)

To determine

To explain why X=0 is same as T>t

g)

Expert Solution

Answer to Problem 29E

X=0 is same as T>t

Explanation of Solution

Given:

X be the event that occurs in a t-second interval.

Calculation:

Here, X=0 mean there are no events occurred in t second. That is, the amount of time that elapses until the next event will be greater than t.

That’s why X=0 is same as T>t.

h)

To determine

To show that P(X=0) is same as P(T>t)

h)

Expert Solution

Answer to Problem 29E

P(X=0) = P(T>1)

Explanation of Solution

Given:

X be the event that occurs in a t-second interval.

Calculation:

Here, X=0 mean there are no events occurred in 1 second. That is, the amount of time that elapses until the next event will be greater than 1.

Therefore, P(X=0) = e−tλ

And P(T>t)= e−tλ

Both are same.

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Answer 2

Question

Chapter 6.3, Problem 29E

a)

To determine

To show that P(X=0) = e−λ

a)

Expert Solution

Answer to Problem 29E

P(X=0) = e−λ

Explanation of Solution

Given:

X be the event that occurs in a 1-second interval.

Calculation:

Let, Probability mass function of Poisson distribution is,

P(X=x)=e−λλxx!

Therefore, just put x =0 in above formula,

P(X=0)=e−λλ00!=e−λ

b)

To determine

To explain why X=0 is same as T>1

b)

Expert Solution

Answer to Problem 29E

X=0 is same as T>1

Explanation of Solution

Given:

X be the event that occurs in a 1-second interval.

Calculation:

Here, X=0 mean there are no events occurred in 1 second. That is, the amount of time that elapses until the next event will be greater than 1.

That’s why X=0 is same as T>1.

c)

To determine

To show that P(X=0) is same as P(T>1)

c)

Expert Solution

Answer to Problem 29E

P(X=0)= P(T>1)

Explanation of Solution

Given:

X be the event that occurs in a 1-second interval.

Calculation:

Here, X=0 mean there are no events occurred in 1 second. That is, the amount of time that elapses until the next event will be greater than 1.

Therefore, P(X=0) = e−λ

And P(T>1)= e−λ

Both are same.

d)

To determine

To show that P(X=0) = e−2λ for 2-second interval.

d)

Expert Solution

Answer to Problem 29E

P(X=0) = e−2λ

Explanation of Solution

Given:

X be the event that occurs in a 2-second interval.

Calculation:

Let, Probability mass function of Poisson distribution is,

P(X=x)=e−2λ(2λ)xx!=e−2λ

Therefore, just put x =0 in above formula,

P(X=0)=e−2λ(2λ)00!=e−2λ

e)

To determine

To explain why X=0 is same as T>2

e)

Expert Solution

Answer to Problem 29E

X=0 is same as T>2

Explanation of Solution

Given:

X be the event that occurs in a 2-second interval.

Calculation:

Here, X=0 mean there are no events occurred in 2 second. That is, the amount of time that elapses until the next event will be greater than 2.

That’s why X=0 is same as T>2.

f)

To determine

To show that P(X=0) = e−tλ for t-second interval.

f)

Expert Solution

Answer to Problem 29E

P(X=0) = e−tλ

Explanation of Solution

Given:

X be the event that occurs in a t-second interval.

Calculation:

Let, Probability mass function of Poisson distribution is,

P(X=x)=e−tλ(tλ)xx!=e−tλ

Therefore, just put x=0 in above formula,

P(X=0)=e−tλ(tλ)00!=e−tλ

g)

To determine

To explain why X=0 is same as T>t

g)

Expert Solution

Answer to Problem 29E

X=0 is same as T>t

Explanation of Solution

Given:

X be the event that occurs in a t-second interval.

Calculation:

Here, X=0 mean there are no events occurred in t second. That is, the amount of time that elapses until the next event will be greater than t.

That’s why X=0 is same as T>t.

h)

To determine

To show that P(X=0) is same as P(T>t)

h)

Expert Solution

Answer to Problem 29E

P(X=0) = P(T>1)

Explanation of Solution

Given:

X be the event that occurs in a t-second interval.

Calculation:

Here, X=0 mean there are no events occurred in 1 second. That is, the amount of time that elapses until the next event will be greater than 1.

Therefore, P(X=0) = e−tλ

And P(T>t)= e−tλ

Both are same.

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Answer 3

Question

Chapter 6.3, Problem 29E

a)

To determine

To show that P(X=0) = e−λ

a)

Expert Solution

Answer to Problem 29E

P(X=0) = e−λ

Explanation of Solution

Given:

X be the event that occurs in a 1-second interval.

Calculation:

Let, Probability mass function of Poisson distribution is,

P(X=x)=e−λλxx!

Therefore, just put x =0 in above formula,

P(X=0)=e−λλ00!=e−λ

b)

To determine

To explain why X=0 is same as T>1

b)

Expert Solution

Answer to Problem 29E

X=0 is same as T>1

Explanation of Solution

Given:

X be the event that occurs in a 1-second interval.

Calculation:

Here, X=0 mean there are no events occurred in 1 second. That is, the amount of time that elapses until the next event will be greater than 1.

That’s why X=0 is same as T>1.

c)

To determine

To show that P(X=0) is same as P(T>1)

c)

Expert Solution

Answer to Problem 29E

P(X=0)= P(T>1)

Explanation of Solution

Given:

X be the event that occurs in a 1-second interval.

Calculation:

Here, X=0 mean there are no events occurred in 1 second. That is, the amount of time that elapses until the next event will be greater than 1.

Therefore, P(X=0) = e−λ

And P(T>1)= e−λ

Both are same.

d)

To determine

To show that P(X=0) = e−2λ for 2-second interval.

d)

Expert Solution

Answer to Problem 29E

P(X=0) = e−2λ

Explanation of Solution

Given:

X be the event that occurs in a 2-second interval.

Calculation:

Let, Probability mass function of Poisson distribution is,

P(X=x)=e−2λ(2λ)xx!=e−2λ

Therefore, just put x =0 in above formula,

P(X=0)=e−2λ(2λ)00!=e−2λ

e)

To determine

To explain why X=0 is same as T>2

e)

Expert Solution

Answer to Problem 29E

X=0 is same as T>2

Explanation of Solution

Given:

X be the event that occurs in a 2-second interval.

Calculation:

Here, X=0 mean there are no events occurred in 2 second. That is, the amount of time that elapses until the next event will be greater than 2.

That’s why X=0 is same as T>2.

f)

To determine

To show that P(X=0) = e−tλ for t-second interval.

f)

Expert Solution

Answer to Problem 29E

P(X=0) = e−tλ

Explanation of Solution

Given:

X be the event that occurs in a t-second interval.

Calculation:

Let, Probability mass function of Poisson distribution is,

P(X=x)=e−tλ(tλ)xx!=e−tλ

Therefore, just put x=0 in above formula,

P(X=0)=e−tλ(tλ)00!=e−tλ

g)

To determine

To explain why X=0 is same as T>t

g)

Expert Solution

Answer to Problem 29E

X=0 is same as T>t

Explanation of Solution

Given:

X be the event that occurs in a t-second interval.

Calculation:

Here, X=0 mean there are no events occurred in t second. That is, the amount of time that elapses until the next event will be greater than t.

That’s why X=0 is same as T>t.

h)

To determine

To show that P(X=0) is same as P(T>t)

h)

Expert Solution

Answer to Problem 29E

P(X=0) = P(T>1)

Explanation of Solution

Given:

X be the event that occurs in a t-second interval.

Calculation:

Here, X=0 mean there are no events occurred in 1 second. That is, the amount of time that elapses until the next event will be greater than 1.

Therefore, P(X=0) = e−tλ

And P(T>t)= e−tλ

Both are same.

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Answer 4

Question

Chapter 6.3, Problem 29E

a)

To determine

To show that P(X=0) = e−λ

a)

Expert Solution

Answer to Problem 29E

P(X=0) = e−λ

Explanation of Solution

Given:

X be the event that occurs in a 1-second interval.

Calculation:

Let, Probability mass function of Poisson distribution is,

P(X=x)=e−λλxx!

Therefore, just put x =0 in above formula,

P(X=0)=e−λλ00!=e−λ

b)

To determine

To explain why X=0 is same as T>1

b)

Expert Solution

Answer to Problem 29E

X=0 is same as T>1

Explanation of Solution

Given:

X be the event that occurs in a 1-second interval.

Calculation:

Here, X=0 mean there are no events occurred in 1 second. That is, the amount of time that elapses until the next event will be greater than 1.

That’s why X=0 is same as T>1.

c)

To determine

To show that P(X=0) is same as P(T>1)

c)

Expert Solution

Answer to Problem 29E

P(X=0)= P(T>1)

Explanation of Solution

Given:

X be the event that occurs in a 1-second interval.

Calculation:

Here, X=0 mean there are no events occurred in 1 second. That is, the amount of time that elapses until the next event will be greater than 1.

Therefore, P(X=0) = e−λ

And P(T>1)= e−λ

Both are same.

d)

To determine

To show that P(X=0) = e−2λ for 2-second interval.

d)

Expert Solution

Answer to Problem 29E

P(X=0) = e−2λ

Explanation of Solution

Given:

X be the event that occurs in a 2-second interval.

Calculation:

Let, Probability mass function of Poisson distribution is,

P(X=x)=e−2λ(2λ)xx!=e−2λ

Therefore, just put x =0 in above formula,

P(X=0)=e−2λ(2λ)00!=e−2λ

e)

To determine

To explain why X=0 is same as T>2

e)

Expert Solution

Answer to Problem 29E

X=0 is same as T>2

Explanation of Solution

Given:

X be the event that occurs in a 2-second interval.

Calculation:

Here, X=0 mean there are no events occurred in 2 second. That is, the amount of time that elapses until the next event will be greater than 2.

That’s why X=0 is same as T>2.

f)

To determine

To show that P(X=0) = e−tλ for t-second interval.

f)

Expert Solution

Answer to Problem 29E

P(X=0) = e−tλ

Explanation of Solution

Given:

X be the event that occurs in a t-second interval.

Calculation:

Let, Probability mass function of Poisson distribution is,

P(X=x)=e−tλ(tλ)xx!=e−tλ

Therefore, just put x=0 in above formula,

P(X=0)=e−tλ(tλ)00!=e−tλ

g)

To determine

To explain why X=0 is same as T>t

g)

Expert Solution

Answer to Problem 29E

X=0 is same as T>t

Explanation of Solution

Given:

X be the event that occurs in a t-second interval.

Calculation:

Here, X=0 mean there are no events occurred in t second. That is, the amount of time that elapses until the next event will be greater than t.

That’s why X=0 is same as T>t.

h)

To determine

To show that P(X=0) is same as P(T>t)

h)

Expert Solution

Answer to Problem 29E

P(X=0) = P(T>1)

Explanation of Solution

Given:

X be the event that occurs in a t-second interval.

Calculation:

Here, X=0 mean there are no events occurred in 1 second. That is, the amount of time that elapses until the next event will be greater than 1.

Therefore, P(X=0) = e−tλ

And P(T>t)= e−tλ

Both are same.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 6.3, Problem 29E

a)

To determine

To show that P(X=0) = e−λ

a)

Expert Solution

Answer to Problem 29E

P(X=0) = e−λ

Explanation of Solution

Given:

X be the event that occurs in a 1-second interval.

Calculation:

Let, Probability mass function of Poisson distribution is,

P(X=x)=e−λλxx!

Therefore, just put x =0 in above formula,

P(X=0)=e−λλ00!=e−λ

b)

To determine

To explain why X=0 is same as T>1

b)

Expert Solution

Answer to Problem 29E

X=0 is same as T>1

Explanation of Solution

Given:

X be the event that occurs in a 1-second interval.

Calculation:

Here, X=0 mean there are no events occurred in 1 second. That is, the amount of time that elapses until the next event will be greater than 1.

That’s why X=0 is same as T>1.

c)

To determine

To show that P(X=0) is same as P(T>1)

c)

Expert Solution

Answer to Problem 29E

P(X=0)= P(T>1)

Explanation of Solution

Given:

X be the event that occurs in a 1-second interval.

Calculation:

Here, X=0 mean there are no events occurred in 1 second. That is, the amount of time that elapses until the next event will be greater than 1.

Therefore, P(X=0) = e−λ

And P(T>1)= e−λ

Both are same.

d)

To determine

To show that P(X=0) = e−2λ for 2-second interval.

d)

Expert Solution

Answer to Problem 29E

P(X=0) = e−2λ

Explanation of Solution

Given:

X be the event that occurs in a 2-second interval.

Calculation:

Let, Probability mass function of Poisson distribution is,

P(X=x)=e−2λ(2λ)xx!=e−2λ

Therefore, just put x =0 in above formula,

P(X=0)=e−2λ(2λ)00!=e−2λ

e)

To determine

To explain why X=0 is same as T>2

e)

Expert Solution

Answer to Problem 29E

X=0 is same as T>2

Explanation of Solution

Given:

X be the event that occurs in a 2-second interval.

Calculation:

Here, X=0 mean there are no events occurred in 2 second. That is, the amount of time that elapses until the next event will be greater than 2.

That’s why X=0 is same as T>2.

f)

To determine

To show that P(X=0) = e−tλ for t-second interval.

f)

Expert Solution

Answer to Problem 29E

P(X=0) = e−tλ

Explanation of Solution

Given:

X be the event that occurs in a t-second interval.

Calculation:

Let, Probability mass function of Poisson distribution is,

P(X=x)=e−tλ(tλ)xx!=e−tλ

Therefore, just put x=0 in above formula,

P(X=0)=e−tλ(tλ)00!=e−tλ

g)

To determine

To explain why X=0 is same as T>t

g)

Expert Solution

Answer to Problem 29E

X=0 is same as T>t

Explanation of Solution

Given:

X be the event that occurs in a t-second interval.

Calculation:

Here, X=0 mean there are no events occurred in t second. That is, the amount of time that elapses until the next event will be greater than t.

That’s why X=0 is same as T>t.

h)

To determine

To show that P(X=0) is same as P(T>t)

h)

Expert Solution

Answer to Problem 29E

P(X=0) = P(T>1)

Explanation of Solution

Given:

X be the event that occurs in a t-second interval.

Calculation:

Here, X=0 mean there are no events occurred in 1 second. That is, the amount of time that elapses until the next event will be greater than 1.

Therefore, P(X=0) = e−tλ

And P(T>t)= e−tλ

Both are same.

Answer 6

Chapter 6.3, Problem 29E

a)

To determine

To show that P(X=0) = e−λ

a)

Expert Solution

Answer to Problem 29E

P(X=0) = e−λ

Explanation of Solution

Given:

X be the event that occurs in a 1-second interval.

Calculation:

Let, Probability mass function of Poisson distribution is,

P(X=x)=e−λλxx!

Therefore, just put x =0 in above formula,

P(X=0)=e−λλ00!=e−λ

Answer 7

Chapter 6.3, Problem 29E

a)

To determine

To show that P(X=0) = e−λ

Answer 8

a)

Expert Solution

Answer to Problem 29E

P(X=0) = e−λ

Answer 9

a)

Expert Solution

Answer 10

a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given:

X be the event that occurs in a 1-second interval.

Calculation:

Let, Probability mass function of Poisson distribution is,

P(X=x)=e−λλxx!

Therefore, just put x =0 in above formula,

P(X=0)=e−λλ00!=e−λ

Answer 13

b)

To determine

To explain why X=0 is same as T>1

b)

Expert Solution

Answer to Problem 29E

X=0 is same as T>1

Explanation of Solution

Given:

X be the event that occurs in a 1-second interval.

Calculation:

Here, X=0 mean there are no events occurred in 1 second. That is, the amount of time that elapses until the next event will be greater than 1.

That’s why X=0 is same as T>1.

Answer 14

b)

To determine

To explain why X=0 is same as T>1

Answer 15

b)

Expert Solution

Answer to Problem 29E

X=0 is same as T>1

Answer 16

b)

Expert Solution

Answer 17

b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given:

X be the event that occurs in a 1-second interval.

Calculation:

Here, X=0 mean there are no events occurred in 1 second. That is, the amount of time that elapses until the next event will be greater than 1.

That’s why X=0 is same as T>1.

Answer 20

c)

To determine

To show that P(X=0) is same as P(T>1)

c)

Expert Solution

Answer to Problem 29E

P(X=0)= P(T>1)

Explanation of Solution

Given:

X be the event that occurs in a 1-second interval.

Calculation:

Here, X=0 mean there are no events occurred in 1 second. That is, the amount of time that elapses until the next event will be greater than 1.

Therefore, P(X=0) = e−λ

And P(T>1)= e−λ

Both are same.

Answer 21

c)

To determine

To show that P(X=0) is same as P(T>1)

Answer 22

c)

Expert Solution

Answer to Problem 29E

P(X=0)= P(T>1)

Answer 23

c)

Expert Solution

Answer 24

c)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Given:

X be the event that occurs in a 1-second interval.

Calculation:

Here, X=0 mean there are no events occurred in 1 second. That is, the amount of time that elapses until the next event will be greater than 1.

Therefore, P(X=0) = e−λ

And P(T>1)= e−λ

Both are same.

Answer 27

d)

To determine

To show that P(X=0) = e−2λ for 2-second interval.

d)

Expert Solution

Answer to Problem 29E

P(X=0) = e−2λ

Explanation of Solution

Given:

X be the event that occurs in a 2-second interval.

Calculation:

Let, Probability mass function of Poisson distribution is,

P(X=x)=e−2λ(2λ)xx!=e−2λ

Therefore, just put x =0 in above formula,

P(X=0)=e−2λ(2λ)00!=e−2λ

Answer 28

d)

To determine

To show that P(X=0) = e−2λ for 2-second interval.

Answer 29

d)

Expert Solution

Answer to Problem 29E

P(X=0) = e−2λ

Answer 30

d)

Expert Solution

Answer 31

d)

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

Given:

X be the event that occurs in a 2-second interval.

Calculation:

Let, Probability mass function of Poisson distribution is,

P(X=x)=e−2λ(2λ)xx!=e−2λ

Therefore, just put x =0 in above formula,

P(X=0)=e−2λ(2λ)00!=e−2λ

Answer 34

e)

To determine

To explain why X=0 is same as T>2

e)

Expert Solution

Answer to Problem 29E

X=0 is same as T>2

Explanation of Solution

Given:

X be the event that occurs in a 2-second interval.

Calculation:

Here, X=0 mean there are no events occurred in 2 second. That is, the amount of time that elapses until the next event will be greater than 2.

That’s why X=0 is same as T>2.

Answer 35

e)

To determine

To explain why X=0 is same as T>2

Answer 36

e)

Expert Solution

Answer to Problem 29E

X=0 is same as T>2

Answer 37

e)

Expert Solution

Answer 38

e)

Expert Solution

Answer 39

Expert Solution

Answer 40

Explanation of Solution

Given:

X be the event that occurs in a 2-second interval.

Calculation:

Here, X=0 mean there are no events occurred in 2 second. That is, the amount of time that elapses until the next event will be greater than 2.

That’s why X=0 is same as T>2.

Answer 41

f)

To determine

To show that P(X=0) = e−tλ for t-second interval.

f)

Expert Solution

Answer to Problem 29E

P(X=0) = e−tλ

Explanation of Solution

Given:

X be the event that occurs in a t-second interval.

Calculation:

Let, Probability mass function of Poisson distribution is,

P(X=x)=e−tλ(tλ)xx!=e−tλ

Therefore, just put x=0 in above formula,

P(X=0)=e−tλ(tλ)00!=e−tλ

Answer 42

f)

To determine

To show that P(X=0) = e−tλ for t-second interval.

Answer 43

f)

Expert Solution

Answer to Problem 29E

P(X=0) = e−tλ

Answer 44

f)

Expert Solution

Answer 45

f)

Expert Solution

Answer 46

Expert Solution

Answer 47

Explanation of Solution

Given:

X be the event that occurs in a t-second interval.

Calculation:

Let, Probability mass function of Poisson distribution is,

P(X=x)=e−tλ(tλ)xx!=e−tλ

Therefore, just put x=0 in above formula,

P(X=0)=e−tλ(tλ)00!=e−tλ

Answer 48

g)

To determine

To explain why X=0 is same as T>t

g)

Expert Solution

Answer to Problem 29E

X=0 is same as T>t

Explanation of Solution

Given:

X be the event that occurs in a t-second interval.

Calculation:

Here, X=0 mean there are no events occurred in t second. That is, the amount of time that elapses until the next event will be greater than t.

That’s why X=0 is same as T>t.

Answer 49

g)

To determine

To explain why X=0 is same as T>t

Answer 50

g)

Expert Solution

Answer to Problem 29E

X=0 is same as T>t

Answer 51

g)

Expert Solution

Answer 52

g)

Expert Solution

Answer 53

Expert Solution

Answer 54

Explanation of Solution

Given:

X be the event that occurs in a t-second interval.

Calculation:

Here, X=0 mean there are no events occurred in t second. That is, the amount of time that elapses until the next event will be greater than t.

That’s why X=0 is same as T>t.

Answer 55

h)

To determine

To show that P(X=0) is same as P(T>t)

h)

Expert Solution

Answer to Problem 29E

P(X=0) = P(T>1)

Explanation of Solution

Given:

X be the event that occurs in a t-second interval.

Calculation:

Here, X=0 mean there are no events occurred in 1 second. That is, the amount of time that elapses until the next event will be greater than 1.

Therefore, P(X=0) = e−tλ

And P(T>t)= e−tλ

Both are same.

Answer 56

h)

To determine

To show that P(X=0) is same as P(T>t)

Answer 57

h)

Expert Solution

Answer to Problem 29E

P(X=0) = P(T>1)

Answer 58

h)

Expert Solution

Answer 59

h)

Expert Solution

Answer 60

Expert Solution

Answer 61

Explanation of Solution

Given:

X be the event that occurs in a t-second interval.

Calculation:

Here, X=0 mean there are no events occurred in 1 second. That is, the amount of time that elapses until the next event will be greater than 1.

Therefore, P(X=0) = e−tλ

And P(T>t)= e−tλ

Both are same.

Answer 62

Ch. 6.1 - Exercises 9-12, fill in each blank with the...Ch. 6.1 - Exercises 9-12, fill in each blank with the...Ch. 6.1 - Exercises 9-12, fill in each blank with the...Ch. 6.1 - Exercises 9-12, fill in each blank with the...Ch. 6.1 - In Exercises 13-16, determine whether the...Ch. 6.1 - In Exercises 13-16, determine whether the...Ch. 6.1 - In Exercises 13-16, determine whether the...Ch. 6.1 - In Exercises 13-16, determine whether the...Ch. 6.1 - In Exercises 17-26, determine whether the random...Ch. 6.1 - In Exercises 17-26, determine whether the random...

To show that P(X=0) = e − λ

Concept explainers

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To show that P(X=0) = e−λ

Answer to Problem 29E

Explanation of Solution

To explain why X=0 is same as T>1

Answer to Problem 29E

Explanation of Solution

To show that P(X=0) is same as P(T>1)

Answer to Problem 29E

Explanation of Solution

To show that P(X=0) = e−2λ for 2-second interval.

Answer to Problem 29E

Explanation of Solution

To explain why X=0 is same as T>2

Answer to Problem 29E

Explanation of Solution

To show that P(X=0) = e−tλ for t-second interval.

Answer to Problem 29E

Explanation of Solution

To explain why X=0 is same as T>t

Answer to Problem 29E

Explanation of Solution

To show that P(X=0) is same as P(T>t)

Answer to Problem 29E

Explanation of Solution

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