MXSuppose a college professor never finishes her lecture before the end of the class period, andalways finishes within five minutes after the class period is supposed to end. Let X = timethat elapses between the end of the class period and the actual end of the lecture. Supposethe pdf of X isf(x) = kx³/2 0 ≤ x ≤ 5 and 0 otherwise.Find the value of k that makes f(x) a legitimate probability density function and use thatvalue of k to find the probability that the lecture ends less than 3 minutes after the classperiod is supposed to end.Please write complete

Answered: Image /qna-images/answer/4f8a55b1-066b-431b-bc11-a7e11f225b88.jpg

Answered: Suppose a college professor never…

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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gn X 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 0.41 (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.) P(X = X) X 0 1 2 3 4 5 6 7 8 (b) Obtain the cumulative distribution function of X. (Round your answers to four decimal places.) F(x) X 0 1 2 3 4 5 6 7 Use the cumulative distribution function of X to calculate P(2 ≤ x ≤ 5). (Round your answer to four decimal places.) P(2 ≤ x ≤ 5) = Need Help? Read It Watch It 4
The score of a student on a certain exam is going to be a number between0 and 1. Think of it as the percentage of correct answers on the exam. Suppose the student passes the exam if their score Sis at least 0.60 and fails otherwise. If the probability density function of a student score S is given by 4x f(a) = 4 4x
Find the cumulative density function for the given probability density function. f(x) = -1/ for 3 ≤x≤7 F(x)=, for 3≤x≤7
A quality index summarizes different features of a product by means of a score. Different experts may assign different quality scores depending on their experience with the product. Let X be the quality index for a tablet. Suppose the respective probability density function is given as follows: cx (2-x) if 0≤x≤2 elsewhere. f(x) = = {₁x2²; 0 (a) Determine e such that f(x) is a proper PDF. (b) Determine the cumulative distribution function. (c) Calculate the expectation and variance of X. (d) Use Tscheby schev's inequality to determine the probability that X does not deviate more than 0.5 from its expectation.
Part B 1) The probability density function is f(x) = 2e-kx i) Standard deviation of x = ?.
Show that the Cauchy probability distribution does not have the first moment that is, E(X) does not exist.
Find the cumulative density function for the given probability density function. 1 f(x) = 4 for 4 ≤x≤8 F(x)=, for 4 ≤x≤ 8
Suppose you have the probability density function if 3 < x < 9 f(x) otherwise Find the cumulative distribution function of X. Select an answer ♥ F(x) if Select an answer if Select an answer Note: When writing your piecewise function, start with the left-most interval.
Suppose a fair coin is tossed 3 times. Define the r.v.'s X = number of Heads and Y = 1(0) if H (T) occurs on the first toss. Find the joint probability function for (X, Y).
Verify that the function corresponding to the following figure is a valid probability density function. Then find the following probabilities:
6 It is given that 25% of the total inventory items in a company's warehouse explains 85% of the value of the inventory. a. What is the parameter A in the Pareto cumulative distribution equation? b. Given 96,1% of inventory value, what is the percent of items give it provided that A is what you found at part a? Select your choice according to part a and b's answer where both of them must be true. a) O a: 0.0521; b:25% b) a: 0.0695; b: 61.56% C) a: 0.0625; b: 85% d) a: 0.0521; b:54.96% e) a: 0.0625; b: 59.17% Leave blank
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

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