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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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Is geometric distribution part of Bernoulli distribution?

Is geometric distribution a type of Bernoulli distribution? But I remember geometric distribution has mean $1/p$ not matching the table here.
spruce
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Distribution of this random variable

What family of distributions does the following cdf belong to? I know this is a dumb question but I've searched for quite a while online coming up empty. $F(x) = \begin{cases} e^{-x^{-\alpha}} & x > 0 \\ 0 & x \leq 0 …
qx123456
  • 575
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How many simultaneous coin tosses until both coins have been heads? Finding a relevant distribution

Consider the following problem. Problem Take two fair coins, A and B. A "round" is when both coins are tossed at the same time. What is the expected number of rounds until both coins have independently been heads at some point? For…
FWDekker
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Probability it takes more then 25 rolls of a six sided die to land on a 6 a total of seven times?

Say you're rolling a die and you continue until you roll a $6$ a total of $7$ times, what is the probability that it takes more than $25$ rolls? The best answer I got was by using the cumulative binomial distribution, so $P(x>25) = 1-p(x<25) = .913$…
koopadaman
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Finding a CDF from a PDF (question about the bounds)

I am doing a problem from my textbook, and I have a question about how they write the answer. The problem is the following If $\begin{align*} f(x)= \begin{cases} 3(1-x)^2, 0 < x < 1\\ 0, \text{otherwise}\\ \end{cases} \end{align*}$ find the cdf…
mXdX
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Proof: Mean of distribution using derivative of normalized condition

Let's assume i'm given a Probability Distribution as follows: $$Bin(n; N, p)=\binom{N}{n}p^n(1-p)^{(N-n)}$$ We know that the mean of this distribution is: $$E[n]=Np$$ However, we want to prove its true using the derivative of the normalized…
pico
  • 941
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Rayleigh Distribution: $P[X > 2] =1 - P[X \le 2] = 1 - F[2]$

My notes give the following explanation of the Rayleigh distribution: The Rayleigh distribution has CDF $F(x) = 1 - e^{-x^2/2}, x > 0$. To get the PDF, we differentiate the CDF, which gives $f(x) = xe^{-x^2 / 2}, \ x > 0.$ For $x \le 0$ both the…
The Pointer
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A random variable N takes integer values 1,2,3,..., where P(N=n)=1/2^n . Find E(N)

A random variable $N$ takes positive integer values $1,2,3,...$ where $P(N=n)=\frac{1}{2^n}$. Find $E(N)$, where $E(N)= \sum_{n=1}^\infty n P(N=n) $.
user9803530
  • 63
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Sum of chi-square and sum of Gaussians

I came up to a point where I needed to add a $\sum_{i=0}^{100}(X_i^2)$, and the $\sum_{i=0}^{100}(X_i)$ where $X_i$ are iid $N(0,1)$. Now, I know that the first term is a chi squared RV with n degrees (n being the number of Gaussian RVs), which can…
Atul Deshpande
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Use Normal Model to approximate the Binomial Distribution

Each item produced in a certain factory is , independently, of acceptable quality with probability $0.95$. Approximate using a normal random variable the probability that at most 9 of the next 200 items are unacceptable. Let $X$ equal to the number…
user59036
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Gamma Distribution Integral

Without appealing to any Fourier inversion results, I'd like to show \begin{align*} \frac{1}{2\pi} \int_{\mathbb{R}} e^{-ity} (1-it)^{-\alpha} dt = \frac{1}{\Gamma(\alpha)} y^{\alpha-1} e^{-y}, \end{align*} for $\alpha > 0$, starting from the left…
Daniel Xiang
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Find the expected value of the largest piece of a stick.

A stick of length 2 is broken into two pieces at a uniformly random chose point. What is the expected value of the largest piece? Here is what I have $U(X) = 2-x$ if $0\leq x \leq 1$ $U(X) = x$ if $0\leq x \leq 1$ But how do I proceed to find…
user59036
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What is the probability to be after $n$ random jumps of unit length in space within a distance of radius $r$ from the start?

Assume a particle, at instant 0 at the origin of three dimensional euclidean space jumps at each tick of the clock exactly one unit from its current position into a random direction. By this we mean: any two patches of the same area of the unit…
Alexander Kovacec
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Find the probability density function of Y= min{X, 1 − X }.

Suppose we have $X$, a $\operatorname{Uniform}(0, 1)$ random variable which follows with the probability density function $f_X (x)$. Let $Y = \min\{X, 1 − X \}$. It wasn't asked but I want to find the pdf of $Y$. I think I know how to deal with…
Lakhdar Mohamed Amine
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3 Component Series System

An engineering system consisting of three components is configured as a series system. The components are acting independently of each other with the ith component's lifetime $T_{i}$ having an exponential distribution with rate $\lambda_{i}$, where…
USC
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