Question: If we alternately flip a balanced coin and a coin
If we alternately flip a balanced coin and a coin that is loaded so that the probability of getting heads is 0.45, what are the mean and the standard deviation of the number of heads that we obtain in 10 flips of these coins?
Relevant QuestionsWith reference to Exercise 3.107 on page 108, by how much can a salesperson who spends $12 on gasoline expect to be reimbursed? The factorial moment-generating function of a discrete random variable X is given by Show that the rth derivative of FX(t) with respect to t at t = 1 is µ'(r), the rth factorial moment defined in Exercise 5.11. Prove Theorem 5.6 by first determining E(X) and E[X(X + 1)]. Theorem 5.6 The mean and the variance of the negative binomial distribution are µ = k/θ and σ2 = k/θ(1/θ – 1) Verify the expression given for E[X(X – 1)] in the proof of Theorem 5.7. Use Theorem 5.9 to show that for the Poisson distribution α3 = 1/√λ, where α3 is the measure of skewness defined in Exercise 4.26 on page 129. Theorem 5.9 The moment-generating function of the Poisson distribution is ...
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