Suppose that independent random variablesXandYhave distributionsN(4,11) and

N(6,14), respectively.

(a) Determine c such that Pr(X ≥ c) = 2Pr(X <c).

(b) Find Pr{

4≤(X − Y)2≤16}.

(c) Suppose thatZis uniformly distributed over the interval [a, b]. Determine the

values ofaandbso that E(Y − X) = E(Z) and Var(Y − X) = Var(Z).

I can't do part a or part c. If you could go through either in stages it would be most appreciated. Thanks