quiz8-key

# quiz8-key - 4(2 pt Determine the value of P X = 1 P X = 1 =...

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Quiz 8. November 3, 2010 Seat # _________ Name: ___ < KEY > ___ Closed book and notes. No calculator. Recall: In a multinomial experiment, let X i denote the number of trials that result in outcome i for i = 1, 2,. .., k . (Then X 1 + X 2 + . . . + X k = n .) The random vector ( X 1 , X 2 , . . . , X k ) has a multinomial distribution with joint pmf P( X 1 = x 1 , X 2 = x 2 , . . . , X k = x k ) = x 1 ! x 2 ! . . . x k ! n ! hhhhhhhhhhhhh p 1 x 1 p 2 x 2 . . . p k x k when each x i is a nonnegative integer and x 1 + x 2 + . . . + x k = n ; zero elsewhere. 1. (2 pt) T F X 1 and X 2 are independent. 2. (2 pt) T F Setting n = 2 yields the binomial family of distributions. 3. (2 pt) The factor p 2 x 2 in the multinomial pmf is the probability of an event. State the event (in words or notation). ____________________________________________________________ In x 2 trials, all result in the second outcome. ____________________________________________________________ x y z f X , Y , Z ( x , y , z ) iiiiiiiiiiiiiiiiiiiiiiiii 1 1 1 0.1 1 1 2 0.2 1 2 1 0.3 2 1 1 0.25 2 2 2 0.15 iiiiiiiiiiiiiiiiiiiiiiiii
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Unformatted text preview: 4. (2 pt) Determine the value of P( X = 1). ____________________________________________________________ P( X = 1) = P( X = 1, Y = 1, Z = 1) + P( X = 1, Y = 1, Z = 2) + P( X = 1, Y = 2, Z = 1) = f X , Y , Z (1, 1, 1) + f X , Y , Z (1, 1, 2) + f X , Y , Z (1, 2, 1) = 0.1 + 0.2 + 0.3 = 0.6 ← ____________________________________________________________ 5. (2 pt) Determine the value of P( X = 1 | Z = 1). ____________________________________________________________ P( X = 1 | Z = 1) = P( Z = 1) P( X = 1, Z = 1) hhhhhhhhhhhhh = 0.1 + 0.3 + 0.25 0.1 + 0.3 hhhhhhhhhhhhh = 0.65 0.4 hhhh ← ____________________________________________________________ ______________________________________________________________________ Write on the back any concerns about the weekly quizzes or the course in general. IE 230 – Page 1 of 1 – Schmeiser...
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## This note was uploaded on 04/25/2011 for the course IE 230 taught by Professor Xangi during the Fall '08 term at Purdue.

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