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Math/Stat 354-02 Concepts of Probability and Statistics Solutions for Section 4.3 Fall 2003 Problem 4.3-10 From Table IV, p. 665; P (X < a) = 0.05 corresponds to a = 5.226 (third column, r = 12. If we want P (a < X < b) = 0.90 and we know that 0.05 of the total area lies to the left of a, then we only need find a b that corresponds to P (X > b) = 0.05 which corresponds to P (X < b) = 0.95. From Table IV, P (X < b) = 0.95 corresponds to b = 21.03. Problem 4.3-12 Since θ = 2, the moment generating function corresponds to a χ2 (24) distribution. r = 12 =⇒ r = 24 2 From this we know that a. µ = r = 24 b. σ 2 = 2r = 48 c. P (15.66 < X < 42.98) is found as follows: P (15.66 < X < 42.98) = P (X < 42.98) − P (X < 15.66) = 0.990 − 0.100 = 0.89 using Table IV. 1