Answered: Suppose that one variable, xx, is…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.CR: Chapter 12 Review

Problem 84CR

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Suppose that one variable, xx, is chosen randomly and uniformly from [0, 1], and another variable, yy, is also chosen randomly and uniformly from [0, 2]. What is the probability that x≤y≤2x+1x≤y≤2x+1?

The probability for x≤y≤2x+1x≤y≤2x+1 is?

Expert Solution

Step 1

Given
X is random variable uniformly distributed $[0, 1]$
Y is random variable uniformly distributed $[0, 2]$

The probability distribution function of Uniform distribution $[a, b]$ is $\frac{1}{b - a} a \leq x \leq b$

The probability distribution functions of X and Y are shown below
$f (x) = \frac{1}{1 - 0} = 1 0 \leq x \leq 1 f (y) = \frac{1}{2 - 0} = \frac{1}{2} 0 \leq y \leq 2$

The joint probability distribution function of X,Y is calculated as shown below
$f (x, y) = f (x) * f (y) 0 \leq x \leq 1, 0 \leq y \leq 2 f (x, y) = \frac{1}{2} 0 \leq x \leq 1, 0 \leq y \leq 2$

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