Consider the following joint probability density function of the random variables X and Y:
f(x, y)= {6y 0 o otherwise}
(1) Find the marginal distribution of X and erify that it is a valid density function.
(2) What is the probability that proportion Y is less than 0.5, given that X is 0.7.

Step-by-step explanation:

Given that a joint probability density function of the random variables X and Y: is

To find the marginal distribution of x

1) To find marginal distribution of x, we integrate with respect to y the region of y.

Here region of y is 0<y<x

So pdf of X =

2) P(y<0.5/x=0.7)

X is having a continuous pdf and hence P(x=0.7) =0

(For any continuous distribution at a particular point prob is 0)

So we find that P(y<0.5/x=0.7) does not exist.