A factory is supplied with grain at the beginning of each week. The weekly demand, X thousand tonnes, for grain from this factory is a continuous random variable having the probability density function given by f(x) = {2(1-x) lo 0≤x≤ 1, otherwise. Find (i) the mean value of X, (ii) the variance of X, (ii) the quantity of grain in tonnes that the factory should have in stock at the beginning of a week, in order to be 98% certain that the demand in that week will be met.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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A factory is supplied with grain at the beginning of each week. The weekly demand, X thousand
tonnes, for grain from this factory is a continuous random variable having the probability density
function given by
f(x) =
{2(1-x)
lo
0≤x≤ 1,
otherwise.
Find
(i) the mean value of X,
(ii) the variance of X,
(ii) the quantity of grain in tonnes that the factory should have in stock at the beginning of a week,
in order to be 98% certain that the demand in that week will be met.
Transcribed Image Text:A factory is supplied with grain at the beginning of each week. The weekly demand, X thousand tonnes, for grain from this factory is a continuous random variable having the probability density function given by f(x) = {2(1-x) lo 0≤x≤ 1, otherwise. Find (i) the mean value of X, (ii) the variance of X, (ii) the quantity of grain in tonnes that the factory should have in stock at the beginning of a week, in order to be 98% certain that the demand in that week will be met.
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