Question

Assume that there is a 0.15 probability that a basketball playoff series will last four games, a 0.30 probability that it will last five games, a 0.25 probability that it will last six games, and a 0.30 probability that it will last seven games. Is it unusual for a team to win a series in 7 games?

Answer 1

DATE:24-04-2020.

ANSWER:-------------

Let 'u' be number of games and f(u) is corresponding probability

Hence for u =4; f(4)=0.15

for u=5; f(5)=0.3

for u=6 ;f(6)=0.25

for u=7 ;f(7)=0.3

Hence mean of u==E(u)=uf(u)=4*0.15+5*0.3+6*0.25+7*0.3=5.7

and E(u2)=42*0.15+52*0.3+62*0.25+72*0.3=33.6

also =E(u2)-(E(u))2=33.6-(5.7)2 =1.11

hence =(1.1)0.5=1.053565

from here confidence interval μ±2σ=(5.7±2.107131)=(3.59 ; 7.81)

as winning 7 game falls in our confidence interval , it is not unusual to win 7 games.