Question

The electric vehicle manufacturing company Tesla estimates that a driver who commutes 50 miles per day in a Model S will require a nightly charge time of around 2 hours (120 minutes) on average to recharge the vehicle's battery. Assume that the actual recharging time required is uniformly distributed between 100 and 140 minutes____

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

Answer 1

The probability density function (PDF) for the battery recharging time is a uniform distribution over the interval [100, 140]. The PDF, f(x), is equal to 1/40 within this interval.

Step-by-step explanation:

The probability density function (PDF) for the battery recharging time can be defined as a uniform distribution over the interval [100, 140].

This means that any value within this interval has an equal chance of being the actual recharging time required.

Mathematically, the PDF, f(x), is given by:

f(x) = 1 / (140 - 100) = 1 / 40, for 100 <= x <= 140