[Solution Library] Let X_1, X_2, ..., X_16 be a random sample from b(1,0.3) and Y_1, Y_2, ..., Y_25 be a random sample from b(2,0.7) . The two random samples
Question: Let \(X_{1}, X_{2}, \ldots, X_{16}\) be a random sample from \(b(1,0.3)\) and \(Y_{1}, Y_{2}, \ldots, Y_{25}\) be a random sample from \(b(2,0.7) .\) The two random samples are independent. Let \(U=\) \(\sum_{i=1}^{16} X_{i}\) and \(V=\sum_{j=1}^{25} Y_{j}\)
- Find the p.m.f. of \(U, E(U), \operatorname{Var}(U)\) and \(P(U>7)\).
- Find the p.m.f. of \(V, E(V), \operatorname{Var}(V)\) and \(P(V>27)\).
- Find the distribution of \(W=50-V .\)
- Find exact value of \(P(U-V=10)\) using calculator or Excel.
- Find the normal approximation of \(P(U-V=10)\).
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Solution: Let X_1, X_2, ..., X_n be a random sample from a distribution
(See Solution) Let X_1, X_2, ..., X_n be a random sample from
![[See Solution] Let X_1, X_2, ..., X_n](/images/solutions/MC-solution-library-38482.jpg "[See Solution] Let X_1, X_2, ..., X_n be a random sample from N(0, θ)")
[See Solution] Let X_1, X_2, ..., X_n be a random sample from N(0, θ)
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