Math Problem Statement
Solution
This image appears to contain a mathematical problem in Persian. Let me break down and translate the key components of the problem so we can address it.
The problem seems to involve a moment-generating function and asks for the variance and .
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The first equation shows the moment-generating function:
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The second part mentions finding the variance of and itself, suggesting the problem is asking to derive properties of the distribution of using its moment-generating function.
I will now proceed to work out the solution, including deriving the variance and the value of . Let me know if you need a more detailed explanation of any steps.
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Math Problem Analysis
Mathematical Concepts
Moment-Generating Functions
Probability Distribution
Variance
Formulas
M_X(t) = E[exp(tX)]
Var(X) = E[X^2] - (E[X])^2
M_Y(t) = M_X(at + b) for Y = aX + b
Theorems
Properties of Moment-Generating Functions
Variance Formula
Suitable Grade Level
Undergraduate
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