e) What is the probability that X is> 5? 0.0821 f) What is the probability that X is> 107 0.0067 Enter a number. g) What is the probability that X > 10 given that X > 5?
e) What is the probability that X is> 5? 0.0821 f) What is the probability that X is> 107 0.0067 Enter a number. g) What is the probability that X > 10 given that X > 5?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
Need the ans for g and h
![The lifetime, \(X\), of a particular integrated circuit has an exponential distribution with a rate of \(\lambda = 0.5\) per year. Thus, the density of \(X\) is:
\[ f(x, \lambda) = \lambda e^{-\lambda x} \text{ for } 0 \leq x \leq \infty, \lambda = 0.5. \]
\(\lambda\) is what \(R\) calls the rate.
**Hint:** This is a problem involving the exponential distribution. Knowing the parameter \(\lambda\) for the distribution allows you to easily answer parts a, b, and c, and use the built-in \(R\) functions for the exponential distribution (dexp(), pexp(), qexp()) for other parts. Or (not recommended) you should be able to use the \(R\) integrate command with \(f(x)\) defined as above or with dexp() for all parts.
a) What is the expected value of \(X\)? [2]
b) What is the variance of \(X\)? [4]
c) What is the standard deviation of \(X\)? [2]
d) What is the probability that \(X\) is greater than its expected value? [0.3679]
e) What is the probability that \(X > 5\)? [0.0821]
f) What is the probability that \(X > 10\)? [0.0067]
g) What is the probability that \(X > 10\) given that \(X > 5\)?
h) What is the median of \(X\)?
i) Enter any comments in the text box below.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F913a0921-d398-48e9-845b-58c3dce12c9b%2F43a1fab5-b06e-4747-a40d-7b911fa780ff%2Fsn3ejh_processed.png&w=3840&q=75)
Transcribed Image Text:The lifetime, \(X\), of a particular integrated circuit has an exponential distribution with a rate of \(\lambda = 0.5\) per year. Thus, the density of \(X\) is:
\[ f(x, \lambda) = \lambda e^{-\lambda x} \text{ for } 0 \leq x \leq \infty, \lambda = 0.5. \]
\(\lambda\) is what \(R\) calls the rate.
**Hint:** This is a problem involving the exponential distribution. Knowing the parameter \(\lambda\) for the distribution allows you to easily answer parts a, b, and c, and use the built-in \(R\) functions for the exponential distribution (dexp(), pexp(), qexp()) for other parts. Or (not recommended) you should be able to use the \(R\) integrate command with \(f(x)\) defined as above or with dexp() for all parts.
a) What is the expected value of \(X\)? [2]
b) What is the variance of \(X\)? [4]
c) What is the standard deviation of \(X\)? [2]
d) What is the probability that \(X\) is greater than its expected value? [0.3679]
e) What is the probability that \(X > 5\)? [0.0821]
f) What is the probability that \(X > 10\)? [0.0067]
g) What is the probability that \(X > 10\) given that \(X > 5\)?
h) What is the median of \(X\)?
i) Enter any comments in the text box below.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON