HW 4 Solutions

# HW 4 Solutions - STATW1211.005 TR 02:40P-03:55P Prof. Zhang...

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Prof. Zhang TR 02:40P-03:55P Homework 4 – Solutions Textbook: Probability and statistics for engineering and the sciences (7 th edition) by Jay L. Devore Chapter 4: Question 98 a. P(10 X 20) = b. P(X 10) = P(10 X 25) = c. For 0 X 25, F(x) = . F(x)=0 for x < 0 and = 1 for x > 25. d. E(X) = ; Var(X) = , so σ x = 7.22 Question 107 a. x f(x) 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 0.5 0.4 0.3 0.2 0.1 0.0 b. F(x) = 0 for x < –1 or = 1 for x > 2. For –1 x 2, c. The median is 0 iff F(0) = .5. Since F(0) = , this is not the case. Because < .5, the median must be greater than 0. d. Y is a binomial r.v. with n = 10 and p = P(X > 1) = 1 – F(1) = Question 111 a. From a graph of f(x; μ , σ ) or by differentiation, x* = μ . b. No; the density function has constant height for A X B. c. F(x; λ ) is largest for x = 0 (the derivative at 0 does not exist since f is not continuous there) so x* = 0. d.

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## This note was uploaded on 01/31/2012 for the course STAT 1211 taught by Professor Hernandez during the Spring '08 term at Columbia.

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HW 4 Solutions - STATW1211.005 TR 02:40P-03:55P Prof. Zhang...

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