Suppose a person's score on a mathematics aptitude test Xis a number between 0 and 1 , Similarly ,his score on an aptitude test Y is also a number between 0 to 1 , suppose joint distribution of X and Y is given as follows;

f(x,y)- [ 2x + 3y] for 0 x 1 and 0 y 1

i)Show that f(x,y) is a proper joint probability density function

ii)Find the P (x 0.5 0.5 )

iii)Find the marginal distribution for the randam variable X.

iv)Find the mean of X.

v)What is the probability that y 0.5 given that x 0.5

Are X and Y independent? Explain