hi there, not sure on how to approach this problem. I'm a bit lost.

how can I show that a rv y which can be expressed a function of rv x, say g(x), is true if the variance of y given x is 0.

so basically show

y = g(x) iff var(ylx) =0

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- September 30th 2011, 03:52 PMKumaconditional variance problem
hi there, not sure on how to approach this problem. I'm a bit lost.

how can I show that a rv y which can be expressed a function of rv x, say g(x), is true if the variance of y given x is 0.

so basically show

y = g(x) iff var(ylx) =0 - September 30th 2011, 07:48 PMchisigmaRe: conditional variance problem
- October 1st 2011, 01:44 AMKumaRe: conditional variance problem
- October 1st 2011, 06:06 AMSpringFan25Re: conditional variance problem
if y=g(x) then the pmf of y|x is:

y=g(x) with probability 1

everything else with probability 0.

Now find the expected value and variance using the normal definitions.

**EDIT: ignore this post, im doing the logic the wrong way round.** - October 1st 2011, 06:16 AMchisigmaRe: conditional variance problem
In order to understand the 'core of problem' there is an example of discrete probability function. Let's suppose to have a discrete random variable x that can assume a countable set of values and You know its probability function and that we want to find the mean value of the random variable y=f(x) ...

(1)

If f(*) is a single value function then...

(2)

... so that y has mean value and variance 0. But what does it happen if f(*) is a multivalued function, like for example ?...

Kind regards

- October 1st 2011, 11:46 AMKumaRe: conditional variance problem
hi, thanks for the explanation. So just to make sure I am understanding correctly.

say for example f(x) = x. Thus for each unique value for x, there is only one value for f(x).

but if I had say f(x) = ± sqrt x, then I would have 2 values of f(x) for each x.

so then my µ would be E(YlX=xk) = sigma y * P(X=xk n Y = y)/P(X=xk)

what I don't understand is how this will make var(ylx) = 0?

in order for var(ylx) = 0 I must have E(Y^2lX) = E(YlX)^2 - October 1st 2011, 07:49 PMchisigmaRe: conditional variance problem