The number of goals scored by a team in a match is independent of other matches, and is denoted by the random variable $$\(X\)$$, which has a Poisson distribution with mean 1.36. A supporter offers to make a donation of $$\(\$ 5\)$$ to the team for each goal that they score in the next 10 matches. Find the expectation and standard deviation of the amount that the supporter will pay. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................
Exam No：9709_s21_qp_63 Year：2021 Question No：1
Answer:
\(\lambda=10 \times 1.36[=13.6]\)
\(\mathrm{E}(\) amount \()=5 \times 13.6=[\$] 68\)
\(\operatorname{Var}(\) amount \()=5^{2} \times 13.6[=340]\)
Standard Deviation \(=[\$] 18.4(4)\) (3 s.f.)
\(\mathrm{E}(\) amount \()=5 \times 13.6=[\$] 68\)
\(\operatorname{Var}(\) amount \()=5^{2} \times 13.6[=340]\)
Standard Deviation \(=[\$] 18.4(4)\) (3 s.f.)
Knowledge points:
6.1.2 use the fact that if then the mean and variance of X are each equal to (Proofs are not required.)
6.2.1.1 more contents
Solution:
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