Give a function f(x)f(x) for a≤x≤ba≤x≤b (and zero elsewhere) such that ff is a PDF of a continuous random variable with expected value μ=7μ=7.
Give a function f(x)f(x) for a≤x≤ba≤x≤b (and zero elsewhere) such that ff is a PDF of...
(b) Let X have the pdf x? f(x)= ;-3<x<3, 18 = zero elsewhere. (i) Find the cdf of X
Let , or ,zero elsewhere,be the pdf of X. Find . Show your work! f(x) = 1 /2
o. Consider a random variable X with pdf given by fx(z) = 0 elsewhere. elsewhere. 0 (a) What is c? Plot the pdf (b) Plot the edf of X. (c) Find P(X 0.5<0.3).
6. Consider a random variable X with pdf given by 0 elsewhere. (a) What is c? Plot the pdf. (b) Plot the cdf of X. Find P(X 0.5< 0.3).
Learning Objective - be able to apply a basic property of a continuous probability density function f(x) and work out its expectation E(X) and variance V(X) For the variable X with probability density function (pdf) f(x)= 1 X for 0<x< n 0 elsewhere The value of nNumber Give the following answers to one decimal place The expectation value of X E(X)Number It is possible for the Expected Value of a random variable to be some value that the random variable...
Let X have probability density function f(2)= k(1+x) -3 for 0 < x < oo and f(x) = 0 elsewhere. a. Find the constant k and Find the c.d.f. of X. b. Find the expected value and the variance of X. Are both well defined? c. Suppose you are required to generate a random variable X with the probability density function f(x). You have available to you a computer program that will generate a random variable U having a U[0,...
2. Let X be a continuous random variable with pdf ( cx?, [xl < 1, f(x) = { 10, otherwise, where the parameter c is constant (with respect to x). (a) Find the constant c. (b) Compute the cumulative distribution function F(x) of X. (c) Use F(x) (from b) to determine P(X > 1/2). (d) Find E(X) and V(X).
2. Let X be a continuous random variable with pdf f(x) = { cr", [w] <1, f() = 0. Otherwise, where the parameter c is constant (with respect to x). (a) Find the constant c. (b) Compute the cumulative distribution function F(2) of X. (c) Use F(2) (from b) to determine P(X > 1/2). (d) Find E(X) and V(X).
1. Consider a continuous random variable X with the probability density function Sx(x) = 3<x<7, zero elsewhere. a) Find the value of C that makes fx(x) a valid probability density function. b) Find the cumulative distribution function of X, Fx(x). "Hint”: To double-check your answer: should be Fx(3)=0, Fx(7)=1. 1. con (continued) Consider Y=g(x)- 20 100 X 2 + Find the support (the range of possible values) of the probability distribution of Y. d) Use part (b) and the c.d.f....
o 3.4 For a random variable for which the PDF is (0, x<-1 x> 1 Determine (a) A, (b) μ, (c) o", (d) sh, (e) ku. 3.5 Suppose that (a) Find f(x). (b) Determine,e and o". (c) Find the expected value of e.