Unformatted text preview: / 3) . Calculate V ar ( X ) . 9. A rv X has pgf given by G ( s ) = E ( s X ) = . 1 + . 4 s 4 + . 5 s 16 . Calculate E ( √ X ) . 10. Two fair 6sided dice are rolled. Let X and Y denote the number of dots showing on each die. Let M = max { X,Y } . Calculate P ( M ≤ 2) . Information A Bernoulli ( p ) rv can only take on 1 or 0 with probabilities p and q = 1p , respectively. The geometric ( p ) probabilities are q k1 p,k = 1 , 2 ,... 1 + x + x 2 + ··· = 1 / (1x ) for  x  < 1 The Poisson ( λ ) probabilities are eλ λ k /k ! The multinomial ( N ; p 1 ,...,p k ) probabilities are N ! ( i 1 !) ... ( i k !) p i 1 1 ··· p i k k ,i 1 + ··· + i k = N . Here p 1 + ··· + p k = 1 . k = 2 yields the binomial which may also be thought of as a sum of k iid Bernoulli ( p ) rv’s. 1...
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 Spring '08
 HADASMOSHONOV
 Probability theory, Summation, Dice, Let, fair 6sided dice

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