The StatDem party contests elections in two countries, Statland and Statopia, the proportion of support the party has in each country being modelled by the random variables X and Y respectively. It is thought that the joint density function for the two variables is of the form f(x, y) = (k(x + 2y) for 0 < x < 1,0 < y < 1 O elsewhere for some constant k. Give answers to the following to 2 decimal places. Part a) Find the value of k. Part b) Find the probability that the StatDem party has the support of more than half the population in each country. Part c) Find the marginal density of the support in Statland evaluated at the point X=1/2. Part d) Find the marginal density of the support in Statopia evaluated at the point Y=1/2.

please teach this I do not no notations

Q 4.2. Let (X, Y) be a random variable with the following density: {152-2 0 £x,x (x, y) = { 1. Express E(Y|X) in terms of X. 2. Express Var(XY) in terms of Y. 0 < x < y < 1, otherwise.

QUESTION 3 Suppose that the continuous random variables X and Y have the joint density function 4xy x, y = [0, 1] 0 otherwise f(x, y) = and suppose the expected values of Y is E(Y) Round to 4 decimal places if needed. = 3. Find the variance of Y.