Question 1: (15 points) Suppose X is a random variable with the following pdf 2x if 0≤x≤ a otherwise f(x) = a. (2) Find

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Question 1 15 Points Suppose X Is A Random Variable With The Following Pdf 2x If 0 X A Otherwise F X A 2 Find 1 (34.8 KiB) Viewed 12 times

Question 1: (15 points) Suppose X is a random variable with the following pdf 2x if 0≤x≤ a otherwise f(x) = a. (2) Find a so that f(x) is a proper pdf. Hint: Use the pdf property that f f(x)dx = 1, i.e., the total area under the f(x) curve is equal to 1. b. (2) Find E(X). c. (2) Find var(X). d. (2) Find P(-5 < X < 0.2). e. (3) Find P(0.2 < X < 0.8|X > 0.3). f. (1) Find P(0.3< X < 0.8|X> 0.3). g. (3) Find the 75th percentile of X.