1. Consider a continuous random variable X with the probability density function fx(x) = x C 3≤x≤7, zero elsewhere. a) Find the value of C that makes fx(x) a valid probability density function. b) Find the cumulative distribution function of X, Fx(x). "Hint": 1. To double-check your answer: should be Fx (3)=0, Fx (7)=1. (continued) 100 Consider Y= g(x)= 2. c) Find the support (the range of possible values) of the probability distribution of Y. d) "Hint": e) Use part (b) and the c.d.f. approach to find the c.d.f. of Y, Fy(y). Fy(y) = P(Y≤y) = P(g(x)≤y) = .... Use the change-of-variable technique to find the p.d.f. of Y, fy(y). "Hint": fy(y) = x(g¹(y)) "Hint": dx dy = To double-check your answer: should be fy(y) Fy(y).