# Tagged Questions

63 views

### Operations on Random Variables

It is known that the equivalent resistance of a parallel combination of two resistors is equal to \begin{align*} R = \frac{R_1R_2}{R_1+R_2} \end{align*} which could be also written as ...
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### What is the pdf of $Z=X/\max(X,Y)$ with $X,Y$ exponentials of lambda parameter?

Given $X,Y$ 2 independent r.v.'s both distributed as $\exp(λ)$, what is the pdf of $Z=X/\max(X,Y)$?
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### Pdf of $Z=(XY)^{1/2}$. with X,Y independent r.v. with the same distribution (iid) [closed]

Let be $X,Y$ two independent random variables having the same distribution (the following is the density of this distribution) $$f(t)= \frac{1}{t^2} \,\,\, \text{for t>1}$$ Calculate the ...
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### What's the density of $Z=\max(X,Y)-\min(X,Y)$ with $X,Y$ exponentials of parameter $\lambda$?

Let be $X,Y$ two independent exponential random variables with parameter $\lambda$. What is the pdf of $Z=\max(X,Y)-\min(X,Y)$? Thanks for your help.
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### Convolution of maximum and minimum of uniform random variables

Let $X_1,\ldots, X_n$ be $n$ independent random variables uniformly distributed on $[0,1]$. Let be $Y=\min(X_i)$ and $Z=\max(X_i)$. Calculate the cdf of $(Y,Z)$ and verify $(Y,Z)$ has independent ...
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### Probability Density of Convolution of Two Random Processes or Variables

Suppose that we have two stationary random processes $x(t)$ and $y(t)$ with probability density functions $f_{x}(x)$ and $f_{y}(y)$ respectively. Now suppose we form: $z(t) = x(t) \ast y(t)$ What is ...
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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 ...
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### Convolution of two random variables, help with a proof

I know there are probably several ways to prove it, I'm interesting in this one in particular: Let $X,Y$ be two independent random variables. Then the probability distribution of $X+Y$ is: ...