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 22h comment Calculate the density of $X=X_1*X_2$ using dirac function. Your first density is a special case of a Rayleigh pdf ... but only properly defined if $\gamma = 1$, so why include the parameter $\gamma$? Your second 'pdf' is not a valid pdf at all, as it does not integrate to unity. Perhaps you have entered it with mistakes, or the question is ill-defined. Feb 8 comment Upper bound for difference of Poisson random variables Perhaps the first bound provides some value when $\lambda$ is large, but when $\lambda = 1$ it appears to be mostly useless. As example, when $\lambda =1$, $P(X\geq Y) = 0.394297$, whereas the bound is 0.84. BTW, this problem is the same as finding the difference of two Poissons, which is known as a Skellam Distribution Feb 7 revised Likelihood function for a distribution with both discrete and continuous components typo fix in title Feb 3 comment Moment Estimator Your question does not make sense. Your density (a member of the Pareto family) is only defined (i.e. only integrates to unity) when $\theta = \frac{1}{10}$. And if $\theta$ has to be that value ... well, there is no parameter left; nor any parameter left to estimate. Jan 31 comment PDF of $X = \max\{X_1,X_2\}$, being $X_1$ and $X_2$ independent Normal distributed random variables The pdf of the maximum is given on page 1 of the paper by Nadarajah and Kotz (2008) available here: gwern.net/docs/conscientiousness/2008-nadarajah.pdf Finding a closed form for the CDF might be a bit more tricky. In your case, just set $\rho=0$. Jan 29 comment Random Variable with p.d.f. as product of two $1d$ Gaussians? I am not sure what the OP means. Jan 29 comment Which distribution is fully decided by the first four moments? Any distribution that is a member of the Pearson family is defined by the first 4 moments, so that is a good starting point. If you wish, you can then just exclude those (like the Normal) that are defined by less than 4 moments. Jan 21 comment Compound Distribution — Log Normal Distribution with Log Normally Distributed Mean You are posting a large number of these parameter mix distribution problems, ... so many that working them all out by hand will keep you busy for a while. I suggest you get a computer algebra system, and once you know how to do one, you can do them all ... assuming closed-form solutions exist, and the software can find it. Jan 20 comment two integers are chosen at random between $0$ and $10$ what is the probability that they differ by no more than $5$? I agree with your reading of the question ! And solution as: $\frac{23}{27}$ Jan 20 comment two integers are chosen at random between $0$ and $10$ what is the probability that they differ by no more than $5$? BETWEEN 0 AND 10 ... does not include 0 or 10. Jan 19 comment Expected Value of Maximum of Two Lognormal Random Variables Super. But shouldn't: \begin{align*} E(\max(X, Y)) &= e^{\nu+\frac{1}{2}\tau^2} N\left(-\frac{-\mu+\nu+\tau^2}{\sqrt{\sigma^2+\tau^2}} \right) + e^{\mu+\frac{1}{2}\sigma^2} N\left(\frac{-\nu+\mu+\sigma^2}{\sqrt{\sigma^2+\tau^2}} \right). \end{align*} be \begin{align*} E(\max(X, Y)) &= e^{\nu+\frac{1}{2}\tau^2} N\left(\frac{-\mu+\nu+\tau^2}{\sqrt{\sigma^2+\tau^2}} \right) + e^{\mu+\frac{1}{2}\sigma^2} N\left(\frac{-\nu+\mu+\sigma^2}{\sqrt{\sigma^2+\tau^2}} \right). \end{align*} ... can you check the minus sign ... Jan 18 comment Escaping Prisoner Probability Question A prisoner is trapped in a cell containing three doors. How is he trapped if he has 3 doors? How much food does he have, for these tunnel tours that last 3 days? If he goes missing, and comes back after 3 days, will the guard notice, and move him to another cell that has no doors? Then there is the existential/self-referential problem: how can a tunnel lead back to the same door? If that were the case, you would need 4 doors, not 2 (unless they fed into each other, which you exclude by the different travelling time). In essence, your problem poses more questions than answers. Jan 14 comment Expected Value of Maximum of Two Lognormal Random Variables with One Source of Randomness Given the way you have defined the problem, i.e. $$X=e^{\mu+\sigma Z};\quad Y=e^{\nu+\tau Z};\quad Z\sim N(0,1)$$ you only have 1 random variable $Z$, not two. Do you mean that you have two independent drawings of $Z$, because that is not what is described? Jan 14 revised Expected Value of Maximum of Two Lognormal Random Variables with One Source of Randomness changed log normal to Lognormal, so that it is found in searches Jan 13 comment Let $(X_1 ,Y_1),(X_2 ,Y_2),…,(X_n ,Y_n)$ be a sample from the uniform distribution on a disc $X^2 + Y^2 \leq \theta$, where $\theta$ is unknown. What's your question? Jan 9 revised Is there an analytical answer for the mode of the convolution of two gamma signals typo fix Dec 24 comment Distribution of maximum gap between points OP: your addendum: "I am assuming the points are sorted" ... changes the question entirely. Dec 20 comment Sum of inverse chi squared random variables Can you start by providing the definition (functional form) for your inverse chi-squared distribution. There are multiple competing definitions in the literature. Dec 20 comment How can I find the upper bound of $E(XYZ)$? What has the question about finding an estimate (or estimator) for $E[X Y Z]$ got to do with finding an upper bound on $E[X Y Z]$? Dec 13 comment Whether given variables distirbution or not Best method to determine the distribution is: first read your lecture notes, then check out some worked examples in your textbook ...