Let Y be a continuous rv with pelf: Find the value of c. Sketch the graph of the

Question

Let Y be a continuous rv with pelf: Find the value of c. Sketch the graph of the pelf. Find P(Y 2) and indicate the area on the graph in part (b) corresponding to this probability. Derive the cdf of Y, Fy(y). Use Fy(y) to find P(1 T 2). Show how to obtain fy.(y) from Fy(y). Compute E(Y).

Explanation / Answer

a) int(c*e^(-y), y = 0..) = -ce^(-y) evaluated at y=0.. = c --> c = 1 b) Graph e^(-y). It's a decaying exponential. c) int(e^(-y), y=0..2) = -e^(-y) evaluated at y=0..2 e^0 - e^(-2) 1 - 1/e^2 d) F(y) = integral of the pdf of y F(Y) = int(e^(-y), y=0..Y) = -e^(-y) evaluated at y=0..Y 1 - e^(-Y) e) P(1

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