Suppose that buses arrive are scheduled to arrive at a bus stop at noon but arealways X minutes late, where X is an exponential random variable with probability densityfunction fx(x) Ae-A. Suppose that you arrive at the bus stop precisely at noon.=(a) Compute the probability that you have to wait for more than five minutes for the busto arrive.(b) Suppose that you have already waiting for 10 minutes. Compute the probability thatyou have to wait an additional five minutes or more.

Given: Let X denotes the time in minutes when the bus is late. The random variable X follows…

Answered: Suppose that buses arrive are scheduled…

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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The time, in 100 hours, that a student uses her game console over a year is a random variable X with probability density function x if 0 < x < 1 f(x) = 2x if 1 < x < 2 0 otherwise. The power (in number of kilowatt hours) expended by the student's game console each year is 46X² + 24. For these problems, please ensure your answers are accurate to within 3 decimals. Part a) Find the mean amount of power expended by the student's game console per year. Part b) Find the variance of power expended by the student's game console per year. U
The arrival of an item ordered in Amazon is assumed to follow the exponential distribution with parameter λ. On average, the item is expected to arrive in 2 days. Calculate λ. What is the probability that you will receive the item within the first 24 hours? What is the probability that the item will arrive late after 5 days?
4. The lifetime in hours of an electronic gadget is a random variable having a probability density function of x2 0. Compute the expected lifetime of such a gadget. f(x) = xe-2x
The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20–39 who regularly skip eating breakfast is 0.2380.238. Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size ?=500n=500 of young adults ages 20–39 in the United States. Apply the central limit theorem to find the probability that the number of individuals, ?,X, in Lance's sample who regularly skip breakfast is greater than 126126. You may find table of critical values helpful. Express the result as a decimal precise to three places. Then, Apply the central limit theorem for the binomial distribution to find the probability that the number of individuals in Lance's sample who regularly skip breakfast is less than 9898. Express the result as a decimal precise to three places.
Suppose the lifespan (in months) of a smartphone battery can be modeled as a continuous random variable with CDF F(x) = 1 − e-x/3 x ≥ 0 What is the probability that the battery lasts between 12 to 15 months?
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 85 and 115 minutes. (a) Give a mathematical expression for the probability density function of battery recharging time for this scenario. (b) What is the probability that the recharge time will be less than 108 minutes? (c) What is the probability that the recharge time required is at least 92 minutes? (d) What is the probability that the recharge time required is between 95 and 110 minutes?
We take the point of view that x (measured in days as units) is a continuous random variable. Suppose a fatal airline accident has just been reported on the news. What is the probability that the waiting time to the next reported fatal airline accident is the following? (a) less than 20 days (b) more than 50 days (c) between 30 and 70 days
Let X and Y be independent exponential random variables with parameters 2 and 3. (a) What is the probability that X + Y > 1. (b) Conditional on X + Y = 1, what is the distribution of X.
The life X (in hours) of a battery in constant use is a random variable with exponential density. What is the probability that the battery will last more than 12 hours (h) if the average life is 8 h?
I need help with this probability density function problem. It asks to calculate the probability that the battery lasts longer than 1 hour. Please show work so that I can understand future problems like this.
local gym has only one treadmill machine for cardio exercises. Suppose exponential interarrival times with mean of 2 per hour, and exponential usage times with mean of 30 minutes per customer. Suppose a person has just arrived at 12.00 noon to use Assume your the machine. What is the probability that the next arrival will come before 1.00 pm, between and after 2.00 pm? Note that you have to provide three 1.00 pm and 2.00 pm, answers, one for each. Suppose no customer arrives before 1.00 pm. What is the probability that the next arrival will come between 1.00 pm and 2.00 pm? What is the probability that the number of arrivals between 1.00 pm and 2.00 pm will be zero (one, more than one)?
Three couples and two single individuals have been invited to an investment seminar and have agreed to attend. Suppose the probability that any particular couple or individual arrives late is 0.33 (a couple will travel together in the same vehicle, so either both people will be on time or else both will arrive late). Assume that different couples and individuals are on time or late independently of one another. Let X = the number of people who arrive late for the seminar. (a) Determine the probability mass function of X. [Hint: label the three couples #1, #2, and #3 and the two individuals #4 and #5.] (Round your answers to four decimal places.) 0 1 2 3 4 5 6 7 8 P(X=x) 0 1 2 3 4 5 6 7 0.1350 0.1330 0.2322 0.1965 0.2633 ✓ ✔ (b) Obtain the cumulative distribution function of X. (Round your answers to four decimal places.) F(x) 0.1350 0.268 0.5002 0.6967 x

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