Answered: Obtain CDF of Y, F_Y (y), and draw…

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Obtain CDF of Y, F_Y (y), and draw the sketch.

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.

Chapter13: Probability And Calculus

Section13.CR: Chapter 13 Review

Problem 1CR

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Question

Consider a random variable, Y , which has a quasi-Bernoulli structure.

With probability p ∈ [0, 1] it takes value 0.

With probability (1 − p) it is described by a continuous random variable, X , with the following PDF,

f_X (x)=1+x, x∈[−1,0), −1≤x<0
f_X (x)=1−x, x∈[0,1], 0≤x≤1
f_X (x)=0, otherwise , x>1

Obtain CDF of Y, F_Y (y), and draw the sketch.

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Step 1: Write the given information.

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Step 2: Compute cumulative distribution function of Y, F_Y(y).

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