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3. The weekly demand for propane gas (in 1000s of gallons) from a particular facility is a random variable X with pdf Find the variance of X. f(x)= 1- -{2 (₁- = x² 1≤ x ≤2 otherwise

3. The weekly demand for propane gas (in 1000s of gallons) from a particular facility is a random variable X with pdf Find the variance of X. f(x)= 1- -{2 (₁- = x² 1≤ x ≤2 otherwise

MATLAB: An Introduction with Applications
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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3. The weekly demand for propane gas (in 1000s of gallons) from a particular facility is a random variable X with pdf 4. Find the variance of X. f(x) 1 1- ({² (₁-2) = 1 ≤ x ≤2 otherwise For two random variables X and Y, if E(X) 1, E(X²) = 2, E(Y) : = 2, E(Y2) = 10, E(XY) = 4. What is the value of the variance Var (Y - 2X)?
Transcribed Image Text:3. The weekly demand for propane gas (in 1000s of gallons) from a particular facility is a random variable X with pdf 4. Find the variance of X. f(x) 1 1- ({² (₁-2) = 1 ≤ x ≤2 otherwise For two random variables X and Y, if E(X) 1, E(X²) = 2, E(Y) : = 2, E(Y2) = 10, E(XY) = 4. What is the value of the variance Var (Y - 2X)?
1. 2. Suppose that X and Y have a discrete joint distribution function as follows: xy = 36 Determine the probability P(|X - Y| ≤ 1). f(x, y) 0 1 X Automobile engines and transmissions are produced on assembly lines, and are inspected for defects after they come off their assembly lines. Those with defects are repaired. Let X represent the number of engines, and Y the number of transmissions that require repairs in a one-hour time interval. The joint probability mass function of X and Y is as follows: f(x, y): 2 3 for x = 1, 2, 3; y = 1,2,3 otherwise .12 .02 .01 Y 0 1 2 3 .13 .10 .07 .03 .16 .08 .04 .06 .08 .04 .02 .02 .02 (a) What is the probability that the total number of engines and transmissions that require repairs is no more than 1 in an one-hour time interval? (b) Find the covariance Cov(X, Y).
Transcribed Image Text:1. 2. Suppose that X and Y have a discrete joint distribution function as follows: xy = 36 Determine the probability P(|X - Y| ≤ 1). f(x, y) 0 1 X Automobile engines and transmissions are produced on assembly lines, and are inspected for defects after they come off their assembly lines. Those with defects are repaired. Let X represent the number of engines, and Y the number of transmissions that require repairs in a one-hour time interval. The joint probability mass function of X and Y is as follows: f(x, y): 2 3 for x = 1, 2, 3; y = 1,2,3 otherwise .12 .02 .01 Y 0 1 2 3 .13 .10 .07 .03 .16 .08 .04 .06 .08 .04 .02 .02 .02 (a) What is the probability that the total number of engines and transmissions that require repairs is no more than 1 in an one-hour time interval? (b) Find the covariance Cov(X, Y).
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