A contractor is required by a county planning department to submit 1, 2, 3, 4, or 5 forms (depending on the nature of the project) when applying for a building permit. Let y denote the number of forms required for an application, and suppose the mass function is given by p(y) 5 cy for y 5 1, 2, 3, 4, or 5. Determine the value of c, as well as the long-run proportion of applications that require at most three forms and the long-run proportion that require between two and four forms, inclusive.

Step-by-step explanation:

The given parameters can be represented as:

Solving (a): The value of c

To do this, we make use of the following rule;

Given that:

This is translated to:

Solve for c

(b) The proportions of applications that requires at most 3 forms

This implies that: y = 1,2,3

So, we make use of:

Recall that:

Substitute

So:

Take LCM

Express as percentage

(c) The proportions of applications that requires between 2 and 4 forms (inclusive)

This implies that: y = 2,3,4

So, we make use of:

Take LCM

Express as percentage