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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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