Tagged Questions

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Bounded function of geometric random variable

if X~ Geometric(p), with q=1-p, then show that for any bounded function f with f(0)=0, we have E(f(x)-qf(x)+1)]=0. Our professor asked us to try solving this problem as a good practice but I have no ...
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Accuracy of a Normal Approximation for a Poisson random variable.

compute bound on accuracy of a normal approximation for a poisson random variable with mean 100? I understand what the question is trying to ask me but I have no idea how to approach it and solve it. ...
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How to set covariance for Bivariate Logistic Distribution

This is the logistic distribution of single random variable (taken from Wikipedia). x = random variable mu = mean of all random variables s = variance. Now, I want to do a Bivariate logistic ...
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Random variables with joint density function

Let R be the rectangle $\ \{(x, y); 0 <= x <= 2, 0 <= y<= 1\}$, and let $\ f(x, y) = >k(x^2+ y^2)$ on R and zero elsewhere. (a) Find the value of k which makes f a joint ...
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How can I visualize the sample space of a complicated random experiment?

A sample space $\Omega$ of a random experiment is the set of all possible outcomes $\omega$. When dealing with random variables (which, formally, is a map from $\Omega \mapsto R$), we usually operate ...
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How to find the conditional CDF of an exponential distribution? [on hold]

How does one find the conditional CDF (Cumulative Distribution Function) of an exponential distribution?
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Probability distribution in wireless channel?

Let suppose that I have a random variable $X_{mn}=\sqrt{\left(1/d_{mn}\right)^\alpha}\times h_{mn}$ wherr $d_{mn}$ is a random variable with uniform distribution and $h_{mn}$ is a random variable with ...
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Geometric random variable $X$, $Pr(X\ is\ even) =$?

Original Question: Toss an unfair coin until we get HEAD. Suppose the total number of tosses is a random variable $X$, and $Pr(HEAD) = p$. What is the probability that $X$ is even? Denote this event ...
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Verify that function g is a joint density function of (X,Y) when outcomes outside A are ignored.

I'm currently doing an econometric course. The questions is from a tutorial to be done next week and I'm trying to prepare as much as I can for it. My main problem is trying to understand what the ...
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Mean of a PMF with a variable

I am given the following PMF: and I am asked to find the mean. I'm a bit lost on what to do with the ...
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Use of convolutions to compute the distribution of the sample mean?

Let's consider N i.i.d continuous random variables from some arbitrary distribution. Why do we have to approximate the distribution of the sample mean using the CLT? Why can't we explicitly compute ...
You are given a set T of n non negative real numbers ${t_0, t_1 ... t_n}$ and probabilities $p_0,p_1...p_n$ where $\sum\limits_{i}^{n} p_1 = 1$. Assume $t_0 < t_1 ...< t_n$. Given a random ...