# HW1 - BME 423 HOMEWORK#1 Fall 2006 1 Suppose that a random...

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BME 423 HOMEWORK #1 Fall 2006 1. Suppose that a random variable (RV) X can take on only the values -2, 0, 1, and 4, and that the probabilities of these values are as follows: Pr(X = -2) = 0.4, Pr(X = 0) = 0.1, Pr(X = 1) = 0.3, and Pr(X = 4) = 0.2. Sketch the d.f. of X. 2. Suppose the d.f. of a RV X is as follows: ( 29 2 0 0 1 0 3, 9 3. 1 x F x x x x F F F F = < Find & sketch the p.d.f. of X. 3. In a class of 50 students, the number of students n i of each age i is shown in the following table: Age i n i 18 20 19 22 20 4 21 3 25 1 What is the expected value of the age of a student randomly selected form this class? 4. Suppose that X has a uniform distribution on the interval [0, 2]. Compute the variance of X. 5. Suppose that X has a normal distribution for which the mean is 1 and the variance is 4. Find the value of each of the following probabilities: a. Pr(X ≤ 3); b. Pr(X > 1.5); c. Pr(2 < X < 5); d. Pr(-1 < X < 0.5). 6. Suppose that X has a normal distribution for which the mean is 1 and the variance is 4. Find the value of x that satisfies the each of the following relationships: a. Pr(X < x) = 0.1 (10 th percentile), b. Pr(X < x) = 0.95 (95

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