Question

Analysis of the scores in a football matches in a local league suggests that the total number of goals scored in a randomly chosen match may be modelled by the Poisson distribution with parameter 2.7. The numbers of goals scored in different matches are independent of one another. On Saturday afternoon, 11 matches are played in the league.

Use this information to answer questions 33-35.

1. Find the expected number of matches in which no goals are scored.

2. Find the probability that there are goals scored in all 11 matches.

3. Find the probability that more than 30 goals are scored in total.

Answer 1

for any query in above comment

Define xa no क and goals scores in ith match, the xi jst poisson (2'7). no Then no. of matchen with out of it with goal scored, YN Binomial ( 11, P(x, =0)). 108 PCX,=0) = 11 é?? ·73926. 2. ELY) = Ya no. G matches with out og 11 atleant the seosred, goal Yun Binomial (11, P(4,7) 2. ELVI) = 1* PCX17,99 FaxCo-ea; = 11-'73926 = 10°26074. x = Ixia total no.of goals scores ton pornon cixart), Ep( x 7,30) = P(+7,30 | *~ Pornon (2017) PL - 29.7 52907 7/ 30-297 (29.7 ~ 1-$('05 505) *47805 [ By CLT, bor large ?, x- si ~ N(O), where x~ Poinon (?)]