# hw6 - STAT 225 Homework 6 Due Friday June 12 Comments 1...

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STAT 225 - Homework 6 Due Friday June 12 Comments: 1. This homework is due Friday, June 12 in class, BEFORE class starts. 2. Please remember staple if you turn in more than one page. 3. You must always SHOW ALL WORK. If you do not show your work, you may not receive full credit. Do the following problems. 1. Show that if X U ( a , b ) then V ( X ) = ( b - a ) 2 12 . Guidance: You can use the fact (which we proved in class) that E ( X ) = a + b 2 It would be useful to know that a 3 - b 3 = ( a - b )( a 2 + ab + b 2 )) 2. Page 177, problems 4.48 3. Page 176, problem 4.43 4. Page 183, problem 4.64 (a) 5. Page 183, problem 4.65 6. Let X N (0 , 1). Find E ( e 3 X + e - X 2 / 2 ) Comment: It would be useful to go over the last example about the normal distribution that I presented in class in lecture 14 (6/8). Also, remember that E [ g 1 ( X ) + g 2 ( X )] = E [ g 1 ( X )] + E [ g 2 ( X )] 7. Page 190, problem 4.91 + (c) Given that during the afternoon on a randomly selected day the demand has exceeded 150 cfs, what is the probability that it exceeds 300 cfs?

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