Expectation of normal distribution
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I know this problem is very easy, finding E(x) from the distribution function. I tried to do it by integration by parts, one way I took x to be my first function and the whole exp term to be my 2nd function, but it didn't work, then I split the exponential term to 2 terms combined one with x as my first function and took the second as the 2nd function but it didn't work either. Can someone help me?
Please provide a detailed proof/answer. Justify all your claims.
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The expert examines expectations of normal distributions.
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Please see the attached file.
.f(x) = __1__ exp-( x - μ )^2
√2πσ^2 2σ^2
α
E(x) = ∫ x __1__ exp-(x - μ)^2 dx
-α √2πσ^2 2σ^2
let ( x - μ ) = t ; dx = dt ; dx = √2σ dt
√2σ √2σ
x = √2σ t + μ
Substituting in the above integral we get
α
∫ (√2σ t + μ) { __1__ exp(- t^2 ) }√2σdt
-α √2πσ^2
α
∫ (√2σ t + μ) { __1__ ...
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