2. In commuting to work, a professor must first get on a bus near his house and then transfer to a second bus. If the waiting time (in minutes) at each stop has the density; 0 10 a. Sketch fx(x) b. Show that fx (x) is legitimate c. What is the probbility that total waiting time is at most 3 min? What is the probbility that total waiting time is at most 8 min ? d. e. What is the probbility that total waiting time is between 3 and 8 min? f. What is the probability that total waiting time is either less than 2 min or more than 6 min?
2. In commuting to work, a professor must first get on a bus near his house and then transfer to a second bus. If the waiting time (in minutes) at each stop has the density; 0 10 a. Sketch fx(x) b. Show that fx (x) is legitimate c. What is the probbility that total waiting time is at most 3 min? What is the probbility that total waiting time is at most 8 min ? d. e. What is the probbility that total waiting time is between 3 and 8 min? f. What is the probability that total waiting time is either less than 2 min or more than 6 min?
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
Question 2 only
![1:43
←
MAY
LTE il 34%
& V
Tesy Comp COT UB
June 4, 7:52 AM
College of Technology
Probability and Statistics (EEC338)
Tutorial 03
1. The lifetime of a bulb expressed in weeks is a Rayleigh random variable with
probability density function given by:
2400
fx(x) = 200
x20
x < 0,
(a) Show that fx (x) is legitimate.
(b) Deduce the distribution function Fx (x). Hence or otherwise,
(c) What is the probability that the bulb will not last a full week? What is the
corresponding probability that the bulb lifetime will exceed a full week?
2. In commuting to work, a professor must first get on a bus near his house and then
transfer to a second bus. If the waiting time (in minutes) at each stop has the density;
0≤x<5
25
fx(x)=-
5 ≤x≤ 10
25
0 x <0 or x> 10.
a. Sketch fx(x)
b. Show that fx (x) is legitimate
c. What is the probbility that total waiting time is at most 3 min?
d. What is the probbility that total waiting time is at most 8 min ?
e. What is the probbility that total waiting time is between 3 and 8 min?
f. What is the probability that total waiting time is either less than 2 min or more
than 6 min?
3. The input-output relationship in a system is described by
y = 16e-1,6x
where x is the input and y is the output. The input is in the range of -1≤ x ≤ 2,
and all values in this range occur in an equally likely fashion.
(a) Draw the sample spaces of the input and the output
(b) Find P(Y≤ 16) and P(2≤ Y <20)
4. Find the values of the real constants a and b such that
Fx(x) = [1-a exp(-x/b)]u(x)
is a valid distribution function.
5. A random variable X is Gaussian with #x= 0 and ox=1
(a) What is the probability that IX] > 2?
(b) What is the probability that X > 2?
6. Repeat exercise 3 if x = 4 and ax=2
7. Let X be a random variable with density fx (x). Let another random variable Y be
defined by Y=(X-a)². Find (y) in terms of Fx (x). Hence suppose X is a random
Gaussian variable where
1
-x²
fx(x) =
exp(
(2πσχέ
20x2
Find the probability density function Fy(y)
Tutor: Takembo Clovis (L)
|||
<
O](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe53828e0-fbca-4901-a6df-51fa058b3532%2F723855ff-26af-4563-b9f8-9727a06e4bcc%2Fj3nhhui_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1:43
←
MAY
LTE il 34%
& V
Tesy Comp COT UB
June 4, 7:52 AM
College of Technology
Probability and Statistics (EEC338)
Tutorial 03
1. The lifetime of a bulb expressed in weeks is a Rayleigh random variable with
probability density function given by:
2400
fx(x) = 200
x20
x < 0,
(a) Show that fx (x) is legitimate.
(b) Deduce the distribution function Fx (x). Hence or otherwise,
(c) What is the probability that the bulb will not last a full week? What is the
corresponding probability that the bulb lifetime will exceed a full week?
2. In commuting to work, a professor must first get on a bus near his house and then
transfer to a second bus. If the waiting time (in minutes) at each stop has the density;
0≤x<5
25
fx(x)=-
5 ≤x≤ 10
25
0 x <0 or x> 10.
a. Sketch fx(x)
b. Show that fx (x) is legitimate
c. What is the probbility that total waiting time is at most 3 min?
d. What is the probbility that total waiting time is at most 8 min ?
e. What is the probbility that total waiting time is between 3 and 8 min?
f. What is the probability that total waiting time is either less than 2 min or more
than 6 min?
3. The input-output relationship in a system is described by
y = 16e-1,6x
where x is the input and y is the output. The input is in the range of -1≤ x ≤ 2,
and all values in this range occur in an equally likely fashion.
(a) Draw the sample spaces of the input and the output
(b) Find P(Y≤ 16) and P(2≤ Y <20)
4. Find the values of the real constants a and b such that
Fx(x) = [1-a exp(-x/b)]u(x)
is a valid distribution function.
5. A random variable X is Gaussian with #x= 0 and ox=1
(a) What is the probability that IX] > 2?
(b) What is the probability that X > 2?
6. Repeat exercise 3 if x = 4 and ax=2
7. Let X be a random variable with density fx (x). Let another random variable Y be
defined by Y=(X-a)². Find (y) in terms of Fx (x). Hence suppose X is a random
Gaussian variable where
1
-x²
fx(x) =
exp(
(2πσχέ
20x2
Find the probability density function Fy(y)
Tutor: Takembo Clovis (L)
|||
<
O
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 4 steps with 1 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