# Questions tagged [pdf]

Probability density function (PDF) of a continuous random variable gives the relative probability for each of its possible values. Use this tag for discrete probability mass functions (PMFs) too.

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### Probability mass function of product of two binomial variables

I have two i.i.d. binomial variables $X$ and $Y$ with given $n$ and $p.$ What is probability mass function of $Z = X \times Y$? I need pmf as function $f(Z, n, p).$
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### What is the PDF sum of N random variables

I have N random variables: $X_1,...,X_N$ which are all independent. The PDF (probability density function) of each random variable $f_{X_i}=e^{-a/(x^{2/b})}x^{-(4+b)/b}$. What is the PDF $f_S(x)$ ...
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### pdf from a set of conditional pdfs

I have an interesting problem, i have seen in many text books ways of calculating conditional pdfs but not many where given a set of conditional pdfs for a variable we wish to calculate it's pdf. In ...
I came across the following in some old class notes of mine: if $\chi_{v_{1}}^{2}$ is independent of $\chi_{v_{2}}^{2}$ then $\frac{\chi_{v_{1}}^{2}}{\chi_{v_{1}}^{2}+\chi_{v_{2}}^{2}}\backsim ... 1answer 28 views ### Integrate$\int_{-\infty}^{\infty}\frac{1}{2\pi}e^{(-\frac{1}{2}(\frac{x^2}{4}+4y^2))} dy$I'm trying to integrate$\int_{-\infty}^{\infty}\frac{1}{2\pi}e^{(-\frac{1}{2}(\frac{x^2}{4}+4y^2))} dy\$ using the fact that the integral of any normal PDF is 1. But I'm having trouble completing the ...
I am reading about variational auto encoders, and there is the below loss function: $$l_i(\Theta,\phi) = - {\mathbb{E}}_{z\sim q} \left[\log p_\phi(x_i|z)\right] + KL(q_{\phi}(z_i|x)||p(z))$$ What ...