3. Could you sove this problem below? Thank you so much! 3. Two teams, Team A an

Question

3.

Could you sove this problem below? Thank you so much!

3. Two teams, Team A and Team B, will play in a playoff series against each other. The playoff series is composed of 7 separate games they play against each other. Team A has a 30% chance of winning each game. Let X be the number of games Team A wins (a) What is the distribution of X? (b) In class we suggested a possible "representation" of X in terms of other random variables (call them Xi, say). What is this representation? Explain what the Xi are in terms of each of the 7 games (c) We know a formula for the mean of X. Use the representation to re-derive this formula. (d) Let Y-n - X. Show by the representation formula that Y ~Binomial(n,.7) and provide an interpretation for this result (e) A team wins the overall series by winning a majority (4) of the games. What is the probability that Team A wins the series? Does playing 7 games instead of just 1 game help or hurt Team A?

Explanation / Answer

a) X - number of fames team A wins

X follow binomial distribution with n = 7 , p = 0.3

b)

X= X1 + X2 + ...X7

where Xi = { 1 if the game is won by Team A

                         0 if team A loses

c)

E(X) = np = 7*0.3 = 2.1

d) Y = n - X

Y = number of game won by Team B

since there are total n games

X+ Y = n

Y = n- X

now as probability of winning of Team A = 0.3

so that of Team B = 1-0.3 = 0.7

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