Re: How to solve the probability density of z=ax+w?

On Mar 8, 5:41 pm, hhwolf76 <james.zho...@xxxxxxxxx> wrote:
This is a problem
If p(a=0)=1/2,p(a=1)=1/2
a,x,w are mutually independent. x,w are all normal distribution and their 1st and 2nd moment have been known. E(w)=0

Can I get the probability density of z=ax+w?

If a = 0 then the pdf of z is the same as the pdf of w, call it
P_0(z). If a = 1 then z = x + w, so z has a normal distribution whose
mean is the sum of the means of x and w, and whose variance is the sum
of the variances of x and w. Call this pdf P_1(z).

Then, unless I'm overlooking something, the overall pdf of z should be
1/2*(P_0(z) + P_1(z)) (which is, of course, *not* a normal
distribution).

and can I get E(x|z)?

Not tried to work out that one yet!


Thanks!

--
Hui Zhou


.

Relevant Pages

  • Re: probability density function
    ... The pdf for an x value of 60 for a normal distribution of mean 40 and ... standard deviation 15 is 0.0109 ... The value of 0.164 is the pdf of a normalised distribution (hence at an x ... probability density function for the above value) ...
    (microsoft.public.excel.worksheet.functions)
  • Re: MLE of a restricted RV
    ... Instead of the pdf, consider the cdf. ... derivative of the conditional cdf, I will have the conditional pdf, ... When I looked over the references about censoring ... distribution, say like the normal distribution, to model an rv like ...
    (sci.stat.edu)
  • Re: sum of two correlated non central chi square variables
    ... > variance sigma^2. ... > The problem I want to solve is actually to obtain the pdf of XY+YZ ... > of the sum gets more complicated. ... Questions on products of two independent normals have been asked here ...
    (sci.stat.math)
  • Re: MLE of a restricted RV
    ... normal change of variables requires I restrict the pdf so |X|<1. ... where pdf is scaled by ... Look up the von Mises distribution. ... is "like" a wrapped normal distribution, but I have the feeling this ...
    (sci.stat.edu)
  • Re: How to solve the probability density of z=ax+w?
    ... x,w are all normal distribution and their 1st and 2nd moment have been known. ... If a = 0 then the pdf of z is the same as the pdf of w, ... mean is the sum of the means of x and w, and whose variance is the sum ... I think that this can be done exactly in closed form. ...
    (sci.math)
Loading