Question

Suppose an electric-vehicle manufacturing company estimates that a driver who commutes 50 miles per day in a particular vehicle will require a nightly charge time of around 1 hour and 40 minutes (100 minutes) to recharge the vehicle's battery. Assume that the actual recharging time required is uniformly distributed between 80 and 120 minutes.

Give a mathematical expression for the probability density function of battery recharging time for this scenario.

Answer 1

Solution:

Given:   an electric-vehicle manufacturing company  require a nightly charge time of around 1 hour and 40 minutes (100 minutes) to recharge the vehicle's battery.

the actual recharging time required is uniformly distributed between 80 and 120 minutes.

That is X follows Uniform distribution with parameters a = 80 minutes and b=120 minutes.

That is:

X ~ U ( a = 80 , b = 120 )

We have to give a mathematical expression for the probability density function of battery recharging time for this scenario.

General probability density function of continuous uniform distribution is:

Thus substituting values of a and b we get:

or

( Since 1/40 = 0.025 , you can use any one of 1/40 or 0.025)