Download Problem 4.3-10 Problem 4.3-12

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