**Electric Vehicle Battery Recharging Time Analysis**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 30 minutes (90 minutes) to recharge the vehicle's battery. Assume that the actual recharging time required is uniformly distributed between 70 and 110 minutes.**(a)** Provide a mathematical expression for the probability density function of battery recharging time for this scenario.\[ f(x) = \begin{cases} \frac{1}{40}, & 70 \leq x \leq 110 \\0, & \text{elsewhere}\end{cases}\]**(b)** What is the probability that the recharge time will be less than 101 minutes?[Input Box]**(c)** What is the probability that the recharge time required is at least 79 minutes? (Round your answer to four decimal places.)[Input Box]**(d)** What is the probability that the recharge time required is between 80 and 90 minutes?[Input Box]

Let be the recharge time of the vehicle's battery.Assume that the actual recharging time required…

Answered: Suppose an electric-vehicle…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A person arrives at the side of a single lane, one way street as a car passes by. Consider this time as time 0. There is no traffic lights and no pedestrian lanes in the nearby area. He stands there watching cars pass by. The number of cars to pass by within a period of time cane be modeled using a poison distribution. Suppose the cars pass by the person at a rate of 4.5 cars per minute. Assume that the cars pass by instantaneously. what is the probability that no cars pass by him within a 2 minute window b) if the person had to guess how many cars would pass by in the next five minutes, what number should he guess? Why? c) what is the distribution for the time until the first car passes by him(time is continuous). What is the expected time until the first car passes by him?
4. Let X be a random variable with cumulative distribution function given by: F(r) = 1 – e-Az. Find the probability density function and so the expected value of variable X.
Suppose that 0.7% of male professional golfers use steroids, and that Max is a male professional golfer who has been randomly selected to take a drug test. The test he has been asked to take has a false positive rate of 1% and a false negative rate of 10%. Use Bayes’ rule to calculate the probability that Max actually uses steroids if he tests positive for steroid use. Give your answer as a decimal precise to three decimal places.
Students arrive at a lecture theatre independently. Suppose the number of students arriving in an hour follows a Poisson distribution with mean 10. Let 7 (in hours) be the time required to wait for 5 students to arrive. Derive the probability density function of T.
Please show every step.
If X is exponentially distributed, prove that the probability that X exceed its expected value is less than 0.5
Students arrive one at a time, completely at random, to an advice clinic at a rate of10 per hour. Students take on average 5 minutes of advice but there is wide variation inthe time they need; this variation may be well modeled by the exponential distribution.b. Again assuming one advisor, what is the probability that there are more than tenstudents in the clinic at a random point in time? What is the probability that the timespent in the clinic exceeds 30 minutes?.
Q1. Suppose X is a continuous random variable. Find an example of a probability density function for X giving expected value E(X) = 1 and variance V (X) = 3 if X has . . . (a.) a uniform distribution. (b.) an exponential distribution. (c.) a normal distribution. In each case, if there is no such probability density function, explain why this is so.
Assume the time required to fully recharge an electric car is uniformly distributed between 160 and 220 minutes. What is the expected charge time, E(x)?
Assume that daily evaporation rates (E) have a uniform distribution with a = 0 and b = 0.35 inches/day. Determine the following probabilities:Pr (E ≥0.1) Pr (E ≤ 0.22) Pr (E = 0.2) Pr (0.05 ≤ E ≤ 0.15

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