The Probability Function for the Number of Insurance Policies John

question 36

Essay

The probability function for the number of insurance policies John will sell to a customer is given by
f(X) = .5 - (X/6) for X = 0, 1, or 2
a.Is this a valid probability function? Explain your answer.
b.What is the probability that John will sell exactly 2 policies to a customer?
c.What is the probability that John will sell at least 2 policies to a customer?
d.What is the expected number of policies John will sell?
e.What is the variance of the number of policies John will sell?

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Definitions:

Classical Method

A traditional approach in statistical inference focusing on hypothesis testing and estimation based on fixed sample sizes.

Probabilities

Measures of how likely it is for an event to occur, represented as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

Mutually Exclusive

Refers to events that cannot occur at the same time in probability theory; the occurrence of one event means the other cannot happen.

P(A ∪ B)

The probability that at least one of two events A or B occurs.