probability

Let K be a discrete random variable with PMF
pK(k)=⎧⎩⎨⎪⎪1/3,2/3,0if k=1,if k=2,otherwise.


Conditional on K=1 or 2, random variable Y is exponentially distributed with parameter 1 or 1/2, respectively.

Using Bayes' rule, find the conditional PMF pK∣Y(k∣y). Which of the following is the correct expression for pK∣Y(2∣y) when y≥0?

e^-y/2 / e^-y+e^-y/2 (Answered in full)

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