Question

What is the PDF of $X_1X_2-X_3X_4$ conditionally on $\sum\limits_{k=1}^4X_k=1$, for $(X_k)$ i.i.d. uniform on $[0,1]$?

score 58 · Answer 1 · 2019-01-28 10:41:56

58

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What is the PDF of $X_1X_2-X_3X_4$ conditionally on $\sum\limits_{k=1}^4X_k=1$, for $(X_k)$ i.i.d. uniform on $[0,1]$?

Published on 28 Jan 2019 - 10:41

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79

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score 41 · Answer 11 · 2019-01-29 14:13:03

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52

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score 21 · Answer 15 · 2019-01-29 22:45:47

21

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List Question

What is the PDF of $X_1X_2-X_3X_4$ conditionally on $\sum\limits_{k=1}^4X_k=1$, for $(X_k)$ i.i.d. uniform on $[0,1]$?

substitution in order to find the probability density function

Cosine of a Wiener process

calculating mean of coin toss

how to find pdf $f_X(x)$ from joint pdf $f_{X,Y}(x,y)$

Find the UMVUE of $b^{\mu}$

Express moments in terms of exponential series

calculating $E[3xy]$ in die throw - mostly about the way you perform the calculation

Can the Central Limit Theorem be applied here?

Use Levy's Continuity Theorem to show Poisson Approximation of the Binomial Distribution

If $X$ and $Y$ are random variables following the binomial law of parameters $n,p$ and $n,q$ then does $X+Y$ follow any known law?

Distribution of $|\sin(\Theta)|$ if $\Theta$ is uniform on $(0,2\pi)$ and arcsine distribution

Simple example of a distribution on +ve natural numbers with $\sum_{n=1}^\infty n^2 p_n < \infty$ and $\sum_{n=1}^\infty \sqrt{p_n} = \infty$

Empirical distribution function

Converting kelly game to log-normal distribution

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