Question

Let K be a discrete random variable that can take the values 1 , 2 , and 3 , all with equal probability. Suppose that X takes values in [0,1] and that for x in that interval we have

fX|K(x|k)=⎧⎩⎨1,2x,3x2,if k=1,if k=2,if k=3.

Find the probability that K=1 , given that X=1/2 .

Answer 1

(e^−y/2)/(e^−y+e^−y/2+1/3*(e^−y/3))

Answer 2

Y is not a valid variable in the answer...

Answer 3

4/11