Question

Suppose X and Y are independent where X ~ N(0, 1) and Y ~ Expo(1). Find the moment generating function of W = 4X - Y + 2. M_W(t) =

          Suppose X and Y are independent where X ~ N(0, 1) and Y ~ Expo(1). Find the moment generating function of W = 4X - Y + 2.
M_W(t) =
        
Suppose X and Y are independent where X   N(0, 1) and Y   Expo(1). Find the moment generating function of W = 4X - Y + 2.
MW(t) =

Added by Timothy L.

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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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The moment generating function of the random variable X is given by Mx(t) = exp{2e^t - 2} and that of Y by My(t) = (3/4e^t + 1/4)^10. Assuming that X and Y are independent, find (a) P{X + Y = 2}. (b) P{XY = 0}. (c) E(XY).

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The moment generating function of the random variable X is given by Mx(t) = exp{2e^t - 2} and that of Y by My(t) = (3/4e^t + 1/4)^10. Assuming that X and Y are independent, find (a) P{X + Y = 2}, (b) P{XY = 0}, and (c) E(XY).

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Transcript

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00:01 Hello in the question the solution is x to the power 4 minus 3 x square plus 2 is equal to 0 so let us consider x square is equal to u so we will get u 2 minus 3 u plus 2 is equal to 0 so that means u square minus 2 u minus u plus 2 is equal to 0 so u u minus 2 minus 1 u minus 2 is equals to 0 so we will get u minus 2 u minus 1 that is 0 now u minus 2 equals to 0 that means u equals to 2 therefore x square is equal to 2 so x equals to plus minus root under 2 and u minus 1 is equal to 0 u is equal to 1 x square is equal to 1 so x is equal to plus minus 1 now we go to the second 1 that is 5x square plus 3x is equals to 2.
01:00 So we can write it as 5x square plus 3x minus 2 is equal to 0.
01:06 So 5x square plus 5x minus 2x minus 2 is equals to 0...
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