Three coins $$\(A, B\)$$ and $$\(C\)$$ are each thrown once. - Coins $$\(A\)$$ and $$\(B\)$$ are each biased so that the probability of obtaining a head is $$\(\frac{2}{3}\)$$. - Coin $$\(C\)$$ is biased so that the probability of obtaining a head is $$\(\frac{4}{5}\)$$. Given that $$\(\mathrm{E}(X)=\frac{32}{15}\)$$, find $$\(\operatorname{Var}(X)\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_w20_qp_53 Year：2020 Question No：6(c)
Answer:
\( \begin{array}{l}
\operatorname{Var}(X)=\frac{0^{2} \times 1+1^{2} \times 8+2^{2} \times 20+3^{2} \times 16}{45}-\left(\frac{32}{15}\right)^{2} \\=\frac{8}{45}+\frac{80}{45}+\frac{144}{45}-\left(\frac{32}{15}\right)^{2}
\end{array} \)
\(\frac{136}{225}\) or \(0.604\)
\operatorname{Var}(X)=\frac{0^{2} \times 1+1^{2} \times 8+2^{2} \times 20+3^{2} \times 16}{45}-\left(\frac{32}{15}\right)^{2} \\=\frac{8}{45}+\frac{80}{45}+\frac{144}{45}-\left(\frac{32}{15}\right)^{2}
\end{array} \)
\(\frac{136}{225}\) or \(0.604\)
Knowledge points:
5.4.1 draw up a probability distribution table relating to a given situation involving a discrete random variable X, and calculate E(X) and Var(X)
Solution:
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