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January 14

Value at risk

why does VaR (U²)=VaR²(U) when U is a standard uniformly distributed variable? please explain. Thank you! — Preceding unsigned comment added by 134.184.120.210 (talk) 03:42, 14 January 2015 (UTC)

I'm not quite sure I understand your question. As you will see from our article on Value at Risk, VaR is calculated for an investment or portfolio of investments, and not for a distribution. Is it possible that VaR here means something other than "Value at Risk"? I suspect this is a homework question; if so, please would you supply some additional context. Thanks. RomanSpa (talk) 18:28, 14 January 2015 (UTC)

Comment requested on a power series solution

Talk:Trigonometric functions#Check my work. To me it isn't the most elegant way to get that series, particularly since the time computing each term grows with k².--Jasper Deng (talk) 06:13, 14 January 2015 (UTC)

Normal distribution question

I'm trying to work out $E(X|X>x)$ where $X\sim N(0,1)$. I've obtained $E(X|X>x)=\underset{x}{\overset{\mathrm{\infty }}{\int }}dy\frac{y\exp (-y^2/2)}{2\pi }=\frac{\exp (-x^2/2)}{2\pi }$, but am convinced it's wrong. The reason I think that it's wrong is that the expectation value I'm trying to find does not depend on the sign of $x$, which has to be nonsense. Where am I going wrong?--Leon (talk) 11:49, 14 January 2015 (UTC)

You are considering a variable, X, with probability distribution P(X)=0 for X<x and P(X)=k⋅exp(-X^2/2) for X>x. Choose k such that the total probability is one. Bo Jacoby (talk) 14:01, 14 January 2015 (UTC).

Also, should be $\sqrt{2\pi }$ rather than $2\pi$ (doesn't matter much since it cancels out in normalization). So what you're looking for is

$\frac{\underset{x}{\overset{\mathrm{\infty }}{\int }}\frac{y\exp (-y^2/2)}{\sqrt{2\pi }}dy}{\underset{x}{\overset{\mathrm{\infty }}{\int }}\frac{\exp (-y^2/2)}{\sqrt{2\pi }}dy}=\frac{\underset{x}{\overset{\mathrm{\infty }}{\int }}y\exp (-y^2/2)dy}{\underset{x}{\overset{\mathrm{\infty }}{\int }}\exp (-y^2/2)dy}$

-- Meni Rosenfeld (talk) 17:03, 14 January 2015 (UTC)

Also the value does depend on the sign of x. If x is less than 0 you're including the center the distribution whereas if it is greater you're just including a tail.

That was the OP's point - the final result should have depended on the sign of x. But because he didn't normalize, he got a result which does not - the integrand is odd, so the integral over a symmetric area around the center is 0. -- Meni Rosenfeld (talk) 21:31, 14 January 2015 (UTC)

Why do you have that extra $y$ in the integrand?--80.109.80.31 (talk) 19:44, 14 January 2015 (UTC)

Because we're calculating the mean. -- Meni Rosenfeld (talk) 21:31, 14 January 2015 (UTC)