# Question

We did not study the Bernoulli distribution in any detail in Section 5.3, because it can be looked upon as a binomial distribution with n = 1. Show that for the Bernoulli distribution, µ'r = θ for r = 1, 2, 3, . . ., by

(a) Evaluating the sum

(b) Letting n = 1 in the moment- generating function of the binomial distribution and examining its Maclaurin’s series.

(a) Evaluating the sum

(b) Letting n = 1 in the moment- generating function of the binomial distribution and examining its Maclaurin’s series.

## Answer to relevant Questions

Approximate the binomial probability b(3; 100, 0.10) by using (a) The formula for the binomial distribution and logarithms; (b) Table II. 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 ...If 40 percent of the mice used in an experiment will become very aggressive within 1 minute after having been administered an experimental drug, find the probability that exactly 6 of 15 mice that have been administered the ...A manufacturer claims that at most 5 percent of the time a given product will sustain fewer than 1,000 hours of operation before requiring service. Twenty products were selected at random from the production line and tested. ...Adapt the formula of Theorem 5.5 so that it can be used to express geometric probabilities in terms of binomial probabilities, and use the formula and Table I to (a) Verify the result of Example 5.5; (b) Rework Exercise ...Post your question

0