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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 ...