can anyone help me with those two questions please?

1. (5 pts) a) A coin is tossed 5 times. Let X be the number of Heads on the rst four tosses and Y be the number of Heads on the last two tossed. Find the joint probabilities pij = P(X = 2', Y = j) for all relevant 1' and 3'. Find the marginal probabilities Pi+ and P+j for all relevant 1' and j. b) Find the value of A that would make the function A f (1:, y) a PDF. Where u: )= 3+e=2y, for 15353 and 05951 ,3: 0 otherwise 2. (5 pts) Find the expectation E(X) and variance Var(X) for each of the following random variables: a) X the sum of the outcomes of one roll of three dice. b) Y continuous random variable with PDF g? for U S y S 2 0 otherwise