A boy is to sell lemonade to make some money to afford some holiday shopping. The capacity of the lemonade bucket is 1. At the start of each day, the

he298c

he298c

Answered question

2021-05-13

A boy is to sell lemonade to make some money to afford some holiday shopping. The capacity of the lemonade bucket is 1. At the start of each day, the amount of lemonade in the bucket is a random variable X, from which a random variable Y is sold during the day. The two random variables X and Y are jointly uniform.
Find and sketch the CDF and the pdf of Z which is the amount of lemonade remaining at the end of the day. Clearly indicate the range of Z

Answer & Explanation

firmablogF

firmablogF

Skilled2021-05-14Added 92 answers

Since Z=XY. Range is from [0,1]. So by convolution formula,
fZ(z)=01fX,Y(z+y,y)
=0z2dy=2(y)0z=2z
Therefore,
FZ(z)={0z02x0z11z1

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