# Thread: Question:Means and variances of linear combinations of random variables

1. ## Question:Means and variances of linear combinations of random variables

The length of time, in minutes, for and airplane to obtain clearance for take off at a certain airport is a random variable Y=3X-2, where x has the density function

f(x) = { 1/4e^(-x/4), x>0
0, elsewhere,

Find the mean and variance of the random variable Y.

the answer from the text book are: mean of Y = 10, variance = 144;

anyone know how to get the answers?

2. $\begin{array}{l}
E(Y) = \int\limits_0^\infty {Yf(x)dx} = \int\limits_0^\infty {\left( {3x - 2} \right)f(x)dx} \\
E(Y^2 ) = \int\limits_0^\infty {Y^2 f(x)dx} = \int\limits_0^\infty {\left( {3x - 2} \right)^2 f(x)dx} \\
V(Y) = E(Y^2 ) - E^2 (Y) \\
\end{array}$

,

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# the marginal cost of production is found to be mc=2000-320x 3x^2.where x is the number of units produced.the fixed cost of production is sh18000.find the cost function of the manufacturers fixed the price per unit is at sh 6800.find the revenue function,t

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