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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)
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...
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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
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
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