Question

The joint probability distribution of a two dimensional random variable (X, Y) is given as follows:
f(x,y) = 2x + y, 0<x<1, 0<y< 1
i) Find the marginal density functions of X and Y. (10 marks)
ii) Find the conditional density function of X given Y = y. (10 marks)
iii) Check for the independence of X and Y. (5 marks)​

Answer 1

Answer:

The joint probability distribution of a two dimensional random variable (X, Y) is given as follows:

f(x,y) = 2x + y, 0<x<1, 0<y< 1

i) Find the marginal density functions of X and Y. (10 marks)

ii) Find the conditional density function of X given Y = y. (10 marks)

iii) Check for the independence of X and Y. (5 marks)