7 MATH.3860 201 Prob & Stat I Due March 22 Show all your work. Late homework will not be accepted without prior approval by email. 1. Let f X (x ) = 1 (x + 1)e x , x > 0 and Y U [1, X ]. Use Total Probability to nd P (Y > 0). 2 2. Let f X (x ) = |x |/10, x {2, 1, 1, 2, 4}. (a) Show f X is a probability density function. (b) Find P (X > 0). (c) Find P (X 1). (d) Find the density function for Y = X 2 . 3. Let f X (x ) = 2/x 2 , x > 2. (a) Show f X is a probability density function. (b) Find P (X < 4). (c) Sketch the graph of f X and shade the area represented by the probability in (b). (d) Find FX and sketch its graph. (e) Find the density function for Y = X 2 . ( f ) Find the density function for Z = 1/X . (g) Use the density function for Z to nd P (Z > 1/4) your answer should agree with (b)