Example 20 : If the probability density function of X is given by(x/2,for 0 < x <1|1/2, for 1< x <2f(x) =(3 – x) i 2, for 2 < x<30, elsewhereFind the expected value of f(x) = x – 5x+ 3

Answered: Image /qna-images/answer/e8f3cfa2-8bea-4cef-9d45-5142d0e48950.jpg

Answered: |Example 20 : If the probability…

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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b) Suppose that X is a random variable with the probability density function given by f(x) = {2(1- (2(1-x), 0≤x≤1 otherwise Find the density function of W = 2X - 1 using method of cumulative distribution function.
A random variable X has the following probability density function k, 0
6.The continuous random variable X has the probability density function given by 1 -2 < x < 4 f(x) = otherwise Determine P(X < 2)
4. Let x be a continuous random variable with the following probability density function 3 (2 – x) 0 < x< 2 f (x) = else (a) Find E(x) (b) Find Var(x)
6. Roughly, speaking, we can use probability density functions to model the likelihood of an event occurring. Formally, a probability density function on (-x, o0) is a function f such that f(r) 20 and (2) = = 1. (a) Determine which of the following functions are probability density functions on the (-x0, 00). fr-1 00 (b) We can also use probability density functions to find the erpected value of the outcomes of the event - if we repeated a probability experiment many times, the expected value will equal the average of the outcomes of the experiment. (e.g. rf(x) dr yields the expected value for a density f(r) with domain on the real numbers.) Find the expected value for one of the valid probability densities above.
Q 3. (a) If the joint probability density function of X and Y is given by | 24:ry for 0 0.
The time, X, for clearing side effects of water purification, in days, has the following cumulative distribution F: 1 F(x) = 0 for x 9 2 a) What is the probability density function for X for 1 5? c) What is the probability X 7? e) What is the probability that X > 6.3? f) What is the probability that X > 7 given the X > 6.3? g) Calculate the 70th percentile of X. h) What is the expected value of X? i) What is the expected value of x2 ? j) What is the variance of X? k) What is the probability that X is more than 0.1 below its expected value?
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.

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|Example 20 : If the probability density function of X is given by (x/2, for 0 < x SI |1/2,for 1< x<2 f(x)= ! (3– x) i 2,for 2 < x<3 0, elsewhere Find the expected value of fx) = x – 5x +3 %3D