Question: LetKbe a discrete random variable with PMF pK(k)= 1/4, ifk=1, 1/2, ifk=2, 1/4, if k=3, 0 otherwise. Conditional onK=1,2,or3, random variableYis exponentially distributed with parameter1,1/2,

LetKbe a discrete random variable with PMF

pK(k)=

1/4, ifk=1,

1/2, ifk=2,

1/4, if k=3,

0 otherwise.

Conditional onK=1,2,or3, random variableYis exponentially distributed with parameter1,1/2, or1/3, respectively.

Using Bayes' rule, find the conditional PMFpKY(ky). What is the correct expression forpKY(2|y), wheny0?

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