Question

A contractor is required by a county planning department to submit one, two, three, four, or five forms (depending on the nature of the project) in applying for a building permit. Let Y 5the number of forms required of the next applicant. The probability that y forms are required is known to be proportional to y—that is, p(y) 5 ky for a. What is the value of k? [Hint: o5 y5 y 51, . . . , 5].

Answer 1

The value of k for the probability function p(y) = ky is 1/15. This ensures that the probability is directly proportional to y and the total probability sums to 1.

Step-by-step explanation:

The question pertains to finding the value of k for a probability function p(y) = ky where y can take values 1, 2, 3, 4, or 5 and the probability is directly proportional to the number of forms y. Since the sum of all probabilities must equal 1, we can write the equation:

1 = k(1) + k(2) + k(3) + k(4) + k(5) = k(1+2+3+4+5).

This simplifies to 1 = k * 15, hence k = 1/15. Therefore, the probability for any value of y is given by p(y) = (1/15)y.