We are required to conduct a poll in a town where on average we know that 40% of the population agrees and 60% disagrees with a new town decree. If we interview 10 people (randomly chosen) solve for the following.

a. What is the probability that exactly 3 people out of the 10 interviewed will agree?

b. What is the probability that the first three people interviewed will agree, and the other seven disagree? Poisson processes and some applications. In this chapter, we have seen that if we relax the assumption that an event occurs exactly in a separate period of time, like in the Bernoulli independent experiments and binomial distribution, we can use the Poisson distribution, given by: P½X ¼ x ¼ e l lx x! with EðXÞ ¼ l: We can model therefore the number of occurrences of a happening in a period of time of length t with a Poisson distribution with parameter l ¼ vt. If the random variable Z(t) denotes the number of occurrences of the happening in a time interval of length t, then: P½ZðtÞ ¼ z ¼ e vtðvtÞ z z! for z ¼ 0; 1; 2; . Solve the following exercises using the Excel random number generator tool.