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Let us say that $P$ is a normal random variable having expected value $\mu$ and variance $\sigma^2$. I am asked to compute the expected value of the variable $Y = |P|$.

Could someone explain?

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    You need to know more that the information given. Are you sure it wasn't $y = |p|^2$?2012-01-22
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    Jensen's inequality gives you a simple upper bound since $$\mathbb E Y = \mathbb E \sqrt{P^2} \leq \sqrt{\mathbb E P^2} = \sqrt{\mu^2 + \sigma^2} \> .$$2012-01-22
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    I am sure about the question. it is to compute the expected value of variable Y=|P|.2012-01-22
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    Do you know something about the *distribution* of $P$? Perhaps it is normal? Or something else? Without further information a definitive answer is not possible. (Consider for example, if $\mathbb P(P=1) = \mathbb P(P=-1) = 1/2$ vs. the case where $P$ is standard normal. Both have mean zero and variance 1, but $\mathbb E |P|$ is different in the two cases.)2012-01-22
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    P is a normal random variable2012-01-22
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    Related: http://math.stackexchange.com/questions/67561/the-expectation-of-the-half-normal-distribution2012-01-22
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    I went through the similar question you directed me to. so here's what I think and what i would like to further clarify.2012-01-22
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    okay before i proceed will this be a discreet or continuous random variable?2012-01-22

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