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groupactivity1solutions

groupactivity1solutions - STAT 380 Group Activity 1...

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STAT 380 Group Activity 1 Solutions 1. ( 10 pts)Four cards will be dealt from the top of a well-shuffled deck. You have the choice of two bets: A. Win if you get a club, diamond, heart and spade IN THAT ORDER B. Win if you get four different suits in the four draws, IN ANY ORDER. Calculate the chance of winning each bet. Which bet do you have a better chance of winning? Bet A: P(win)=P(CDHS)= 13 13 13 13 . . . 0.0044 52 51 50 49 = Bet B: P(win)=P(CDHS or CSHD or …(all possible arrangements of C,D,H,S)) =4!* 13 13 13 13 . . . 52 51 50 49 ( or 52 39 26 13 . . . 52 51 50 49 )=0.1055 So you have 24 times of winning Bet B as compared to Bet A. 2. (15 pts) The average length of stay in a hospital is useful for planning purposes. Suppose that the following is the probability distribution of the length of stay in a hospital after a minor surgery: Days 2 3 4 5 6 Prob 0.1 0.4 0.25 k ( k -0.05) The value of k is ___ 0.15 _______. The average length of hospital stay after minor surgery is _____ E(X)= ( ) x xf x =_3.75 ___. The variance of the distribution of length of hospital stay is ___ Var(X)=E(X 2 )- [E(X)] 2 =_1.2875 ____ 3. a. (8 pts) Let X and Y be discrete random variables with joint p.m.f.
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