This preview shows page 1. Sign up to view the full content.
Unformatted text preview: . 9, that the class average would be within 5 of 75? Problem 3 Suppose now this professor believes that the test score of a student taking her nal examination is a NORMAL distributed random variable with the same mean 75 and the same variance 25. (a) Compute the probability that a students test score will exceed 85. (b) Compute the probability that a student will score between 65 and 85? (c) How many students would have to take the examination so as to ensure, with probability at least . 9, that the class average would be within 5 of 75? Compare those with the results in problem 2. The following problem is optional for 3500 students, mandatory for students enrolled in 5500 Problem 4 If X is a random variable with moment generating function X , show that (a) X (2 t ) X ( t ) 2 for all t (b)For a constant a > 0, P [ | X | a ] e-ta | X | ( t ) , t > . 1...
View Full Document
- Summer '08