Question: The bi-dimensional variable (X,Y) has a probability distribution represented by the density function:

f (x,y) = 6 ⁄ 5 * ( x + y²) where, 0≤x≤1 and 0≤y≤1

a.) Calculate the average value and the variance of the marginal distribution of X

b.) Calculate the covariance

c.) Determine whether or not the variables are stochastically independent

d.) Calculate the probability: P [( Y≤0.3 ) ∩ ( X ≥ 0.6 )]