The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3.

#3ai) Refer to information above: The random variable x satisfies which of the following probability distributions? Explain

#3aii) Refer to information above: The appropriate probability distribution for the random variable is what? Explain

#3b) The prior probabilities for events A₁, A_2, and A₃ are P (A₁) = .20, P (A₂) = .50, and P (A₃) = .30. The conditional probabilities of events B given A₁, A_2, and A₃ are P (B | A₁) = .05, P (B | A₂) = .40, and P (B | A₃) = .30.

#3bi). Compute P (B A₁), P (B A₂), and P (B A₃).

#3bii). Compute the posterior probability of P (A₂ | B).