- #1
ionlylooklazy
- 30
- 0
conditional density function - need help please!
given
a signal x, is a random variable which is expontential with a mean of 3. it is transmitted through an additive gaussian noise channel, where the gaussian noise has a mean of -2 and a variance of 3. the signal and noise are independent.
Find an expression for the CDF (conditional density function) of the signal given the observation of the output. fx(x|y)
what i think...
from bayes theorem i know:
fx(x|y) = fx(y|x)*fx(x) / fy(y)
assuming:
output = y
noise = n
input = x
y = n+x
how do i find fx(y|x) ?
the only info i have are the probability density function's for x and n
also every attempt at convoluting the exponential with the guassian (to find y) has failed whether by hand, calculator, or matlab
given
a signal x, is a random variable which is expontential with a mean of 3. it is transmitted through an additive gaussian noise channel, where the gaussian noise has a mean of -2 and a variance of 3. the signal and noise are independent.
Find an expression for the CDF (conditional density function) of the signal given the observation of the output. fx(x|y)
what i think...
from bayes theorem i know:
fx(x|y) = fx(y|x)*fx(x) / fy(y)
assuming:
output = y
noise = n
input = x
y = n+x
how do i find fx(y|x) ?
the only info i have are the probability density function's for x and n
also every attempt at convoluting the exponential with the guassian (to find y) has failed whether by hand, calculator, or matlab
Last edited: