yes just find the distribution of X, the PMF (discret case)
then calulate the probability like this:
P(Y)=E[1/X]=sum_{i=1}^{i=n}{(1/i)*P(X=i)}
using Jenesen inequality here doesn't help because the funtion is defined to be 0 at 0 so we can't consider it convex.
hope that would help
hi all
yes P(Y) is another event which probability is the expected value of other function of random variable.
Applying Jenesen Inequality does not help because it gives the lower bound.
So I decided to work on the problem to get X distribution to calculate the E[1/(1+X)]
but few days later I...
Hello all
I have a question about Markov chain I've obtained in an application.
There is no need to mention the application or the details of markov chain because my question is simply:
The transition probabilities are derived with equations that depend on the stationary probability, I know...
I know dear
that's why I asked about why setting Y=0 when X=0 caused the problem
You said the function is not convex any more, here I didn't get it, does it mean now it's concave?
the second derivative is positive since X>0
Anyway thanks for reply I'll do more research on that
Yes you are right to assume it but in the calculation I assumed X>0 when calculating Y.
Even with this assumption I can't approve the opposite inequality.
This can be thought like: choosing one message from X messages problem.
Thanks for reply
Hi everyone
I don't know if I can find someone here to help me understand this issue, but I'll try
the jensen inequality can be found here http://en.wikipedia.org/wiki/Jensen%27s_inequality
I have the following discrete random variable X with the following pmf:
x 0...
Hi all
Sorry for reposting, the previous post wasn't clear enough, it's my mistake, I'll make the question more clear, I found lot of people asking the same question on the Internet.
Given that X is random variable that takes values:
0.....H-1
The PMF of X is unknown, but I can tell...
I think what chiro said makes sense for me right now
X 0 1 2 3 ...H
P(Y|X=i)=1/i 1 0.5 1/3 ...1/H
From the second line I'll try to estimate the PMF of Y using MLE, I'll try it
hi micromass
Actually X is discrete I need to say: X is not uniform but Y=1/X is constructed as a uniform distribution from X, that means gives that X=3 then Y=1/3
P(y)=E[1/X]
I know only X then I need to get E[1/X] using only E[X] which is known but the distribution of X is not known.
Thanks...
hello chiro
Thanks for replying
I have a background with Random Variables and stochastic processes
I've read about MLE once but never use it in my applications, I remember that it is used to estimate the random variable from sample data vectors.
which is not what I'm looking for...
Hi all
I'm looking for solving this problem to find the closed form solution if it is possible:
Y=\frac{1}{X}
Where X is uniform random variable > 0
I know the expected value for X which is \overline{X}
is there a method to find the expected value of Y which is \overline{Y} in term of...