please help to solve this

Reply Fri 22 Jul, 2022 06:52 am
If (X,Y) are discrete random variables with values x,y=0,1 and the joint PMF is defined by f(0,0)=1/4, f(0,1)=1/8, f(1,0)=1/2, f(1,1)=1/8, what are the values of the conditional PMF, f(y|x=1), of Y given X=1?

a). f(0|1)=3/8, f(1|1)=5/8
b). f(0|1)=1/5, f(1|1)=4/5
c). f(0|1)=5/8, f(1|1)=3/8
d). f(0|1)=4/5, f(1|1)=1/5

Reply Fri 22 Jul, 2022 09:26 am
The answer is D.

Let's say you run this eight times. Based on the Probability Mass Function for X and Y, you will get (0,0) two times, (0,1) one time, (1,0) four times and (1,1) just one time.

Now you know that X=1, so you just have (1,0) four times and (1,1) one time. This is option D, four out of five times you will have (0,0) and one of five you will have (1,1)
Reply Fri 22 Jul, 2022 10:34 am
thank you so much
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