Question

1. Consider a continuous random variable X with the probability density function Sx(x) = 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”: To double-check your answer: should be Fx(3)=0, Fx(7)=1. 1. con (continued) Consider Y=g(x)- 20 100 X 2 + Find the support (the range of possible values) of the probability distribution of Y. d) Use part (b) and the c.d.f. approach to find the c.d.f. of Y, Fy(y). "Hint": Fy(y) = P(Ysy) - P(g(x)sy) = .... e) Use the change-of-variable technique to find the p.d.f. of Y, fy(y). "Hine": fy(y) – fx(8-'(x)) by "Hint": To double-check your answer: should be y(y) - Fy(y).

Answer 1

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