Question

you have three routes to get to work in the morning time is a random variable that follows has the following density function: f (x) = k / x ^ 4, x> 15

a) Find the appropriate value for the constant k and graph the density function.

b) Find and graph the cumulative probability function.

c) Calculate the probability of arriving in less than 25 minutes.

d) What is the probability of arriving in exactly 25 minutes?

e) Calculate the expected value and the variance of time.

f) What is the time exceeded only for 10% of the days?

Answer 1

We would be looking at the first four parts here as:

a) The sum of all probabilities across the X range should be 1. Therefore, we have here:

Therefore 10125 is the required value of k here.

The PDF thus is graphed here as:

b) The CDF for X here is obtained as:

This is the required CDF for X here.

c) The probability here is computed as:

Therefore 0.784 is the required probability here.

d) The probability of coming in exactly 25 mintues is computed here as:

therefore 0.02592 is the required probability here. '