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 ﬁnal examination is a NORMAL distributed random variable with the same mean 75 and the same variance 25. (a) Compute the probability that a student’s 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 φ X , show that (a) φ X (2 t ) ≥ φ X ( t ) 2 for all t (b)For a constant a > 0, P [  X  ≥ a ] ≤ eta φ  X  ( t ) , ∀ t > . 1...
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 Summer '08
 WEBER
 Normal Distribution, Probability theory, probability density function, moment generating function

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