7. a) Suppose that X is a uniform continuous random variable where 0 < x < 5. Find the pdf f(x) and use it to find P(2
7. a) Suppose that X is a uniform continuous random variable where 0 < x < 5. Find the pdf f(x) and use it to find P(2
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
![7. a) Suppose that X is a uniform continuous random variable where 0<x<5. Find the pdf f(x) and use it
to find P(2<x<3.5).
Uniform (0.5) = f(x)=1/5
3.5 1
P(2<x<3.5) = √₂5=dx :
- dx = 0.3
b) Suppose that Y has an exponential distribution with mean 20. Find the pdf f(y) and use it to compute
P(18 <Y <23).
-SIS 20
c) Find E(5X + 2) and Var(5X + 2), where X is the random variable given in part (a).
E(5x+2) = 5E(x) + 2 = 14.5
Var(5x+2) = 25var(x) = 52.08
P(18 < X <23) =
23 1 -y/20
= 0.09](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fece3d40f-e8f0-464a-aada-c18e494e1994%2Fdae76085-9b1a-47f8-a7b9-91e197a09bc0%2F44sp3p3_processed.png&w=3840&q=75)
Transcribed Image Text:7. a) Suppose that X is a uniform continuous random variable where 0<x<5. Find the pdf f(x) and use it
to find P(2<x<3.5).
Uniform (0.5) = f(x)=1/5
3.5 1
P(2<x<3.5) = √₂5=dx :
- dx = 0.3
b) Suppose that Y has an exponential distribution with mean 20. Find the pdf f(y) and use it to compute
P(18 <Y <23).
-SIS 20
c) Find E(5X + 2) and Var(5X + 2), where X is the random variable given in part (a).
E(5x+2) = 5E(x) + 2 = 14.5
Var(5x+2) = 25var(x) = 52.08
P(18 < X <23) =
23 1 -y/20
= 0.09
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 5 steps with 39 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Similar questions
- Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON