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Mathematics Stack Exchange

Questions tagged [probability-distributions]

Questions on using, finding, or otherwise relating to probability distributions, probability density functions (pdfs), cumulative distribution functions (cdfs), or other related functions. Use this tag along with the tags (probability), (probability-theory) or (statistics).

Any probability distribution, including beta, binomial, chi, Erlang, gamma, geometric, lognormal, negative binomial, normal (Gaussian), Pareto, Poisson, Student's t, uniform, Wald, Weibull, zeta, and Zipf.

28080 questions
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Use the MFG (Moment Generating Function) technique to determine the joint distribution of (X,Y)

Im given V and W are independent standard normal random variables where $x=\frac{(V+W)}{\sqrt(2)}$ and $y=\frac{(V-W)}{\sqrt(2)}$. This is what I did:…
USC
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Which gamma do I need for my Cauchy distribution?

I need a probability distribution which is the ratio of two normal distributions or $P=(N_1/N_2)$. The mean of both normals can be assumed to be zero, and the variance is known. Apparently the distribution I'm looking for is a Cauchy distribution,…
user1492428
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What is the distribution of $X=F_{X}^{-}(x)$?

For any given $F_X$, show that if $U \sim \text{Uniform}(0,1)$ and $F_{X}^{-}(u) = \text{min}\{x:F_X(x)\geq u\}$ then $X = F_{X}^{-}(U)$ has distribution $F_X$. I tried this and got to $F_X(x) = P(X\leq x) = P(F_{X}^{-}(U)\leq x)$ Not really sure…
mrnovice
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What is the joint probability density function of two independent uniformly distributed random variables between (0,1)?

Let $X,Y$ be independent and uniformly distributed in the interval $(0,1)$. What is the joint probability density function? The answer I get is: $$f_{X,Y}(x,y) = 1,\quad 0
mrnovice
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difference between events represented by random variables X and X-1

let X be a geometric random variable, representing the number of trails up until first heads occurs. so, $X=4$ will represent the event $T_1T_2T_3H_4$ part a given this information, why would $X-1=3$ represent the event $T_2T_3H_4$? isn't $X-1=3$…
abhishek
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Why when we are asked for distribution we always deal with cdfs

General Question, I wonder why every question in a probability exercise where we need to check the distribution of a random variable it always goes by showing the cdf and where it's defined. why we don't show pmf or pdf instead? of course, we can…
Harel Yacovian
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Unimodal PDF having non-unique mode

I am learning statistics from this book and in Exercise 2.27 (on page 79) I came across the term unimodal. As I understand, unimodal means having only one value of mode. But in this question, in part (b), it is asked to give an example of unimodal…
Ankit Seth
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Find the joint distribution of the following random vectors (X, Y); (X, Z); (Y, Z) and (X, Y, Z).

A box contains eight balls numbered from 1 to 8. The first four are red and the other white. We select the balls randomly from the box and define the following variables: X is the number of white balls in the sample, Y the number of even numbers and…
pin_r
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What could this odd probability distribution be?

I performed some computations on a time-series, and when I checked the probability distribution of a result I obtained this odd histogram: I've never seen gothic spires like this. What kind of distributions is this? Are the spires the result of…
Fabio Capezzuoli
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Random Variable PDF with coin tosses.

Hello I am trying to figure out a few parts of the following question: We consider a random selection of coins where the probability of heads, C for the coins is a random variable whose pdf is $ f_c = k*c $ for $ 0 \leq c \leq 1 $. a) Find k. For…
jackana3
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smallest possible size of a sample using the Central Limit Theorem

It appears that in this question I could be missing something or is it? X bar, the mean of a sample of n independent observation of X, is Normally distributed such that P(z > 0.25)< 0.1. Find the smallest possible value of n. Could there be a case…
Waitara Mburu
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CDF and Inverse CDF of Wrapped Cauchy Distribution

The standard wrapped-up Cauchy distribution has the following probability density function: $$f(x,p)= \frac{1-p^2}{2\pi(1+p^2)-2p\cos(x)}$$ where x is from $0$ to $2\pi$ Can anybody know, what is the CDF and InvCDF of this distribution? Can you…
WasMaths
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Probability fail increase next attempt with variations

I have $3$ choices to make a attempt: first one costs $460$, and has a $10\%$ chance of success, and if it fails, it has a $3\%$ increase in chance for the next attempt. The second costs $1430$, and has a $30\%$ chance, and if it fails, has a $9\%$…
icezxy
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notation for probability distribution (double absolute)

I am trying to understand this term in an equation, but I am somehow confused. Can someone clear it for me ? $KL(q_2(z_2|x_2)||p_{\eta}(z))$
Mostafa Hussein
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Probability distribution type of the following variable

I'm not sure to which Probability distribution type the variable "Number of previous times defaulted on loan repayment" belongs to. I was thinking of Geometric distribution. Can someone please clarify this. Thanks!
user9815591
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