Mathematics Stack Exchange
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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Approximating a binomial distribution by the corresponding normal distribution

A fair coin is tossed 10 times. Find the probability of getting at least 4 heads and at most 6 heads. Let X be the probability distribution of getting x heads. We need to find $k$ such that $k = P(4 \le X \le 6)$. It is a binomial distribution with…
Mick
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find the cummulative distribution function FX(x) given an image above

Suppose we have a street intersection. It consists of a center point and 4 one-mile-long streets from the center. Street 1 points up, street 2 points down, street 3 points to the right and street 4 points to the left. The city assigns an ambulance…
Alice
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Distribution of sum of independent random variables

Let $X$ and $Y$ be independent random variables taking values in $[0,1]$ where $X$ is uniform. Question is, what distribution on $Y$ will yield a uniform distribution on $[0,2]$ for the sum $Z=X+Y$? Somehow, by inspection, since the distribution of…
Ashok
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The probability of no cars passing within a certain time interval

Let's say there is an induction loop in a road capable of counting the number of cars passing over it. By keeping a list of moments for when a car passed the detection loop, I am able to determine the average interval $\mu$ and variance $\sigma^2$…
Roelof van den Berg
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cdf of sum of a discrete and continuous random variable

Let U be uniformly distributed on the interval $(0, 2)$ and let V be an independent random variable which has a discrete uniform distribution on $\{0, 1, . . . , n\}$. i.e. $P\{V = i\} =\frac{1}{n+1}$ for $i = 0, 1, . . . , n.$ Find the cumulative…
kris91
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Question on MGFs & Finding The Distribution of a Sum

Suppose that $X_1$, $X_2$, ..., $X_n$ are independent, where each $X_i$ has probability (mass) function $p_i$($x_i$) given as follows: $p_i$($x_i$) = $\frac{e^{-\lambda}\lambda_i^{x_i}}{x_i!}$ (the parameter $\lambda_i$ differs in the distribution …
tuba09
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Evaluate the expectation of $\frac{1}{UV}$

Another question from the past test papers! The joint density function of $X$ and $Y$ is given by $f_{X,Y}(x,y) = \frac{1}{x^2 y^2}$, $x \geq 1, y \geq 1$. (i) Find the joint density function of $U=XY$ and $V=X/Y$. (ii) What are the marginal…
drawar
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Simulation of a random variable with a simple PDF

Suppose $X$ be random variable with the pdf $f(x)=2x,0\leq x \leq 1.$ How can we simulate $n$ independent instantiations of $X$?Thanks for any answers/hints.Suggestions of relevent books or tutorials are also welcom
AgnostMystic
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What is the distribution of choosing kids from a class?

Given a class of $m$ kids, $\frac{m}{2}$ boys and $\frac{m}{2}$ girls. Their teacher Erica randomly choosing kids from her class one by one. Define success in the experiment when Erica chose at least one boy and at least one girl. Suppose $Y$ is the…
Dan
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How to find set functions that satisfy two of the three properties (probability)

We know from the theory the following properties: 0≤P(A)≤1 for every A P(Ω)=1 If A1, A2,...An are mutually exclusive then P(A1 ∪ A2 ∪ ...An)= P(A1)+P(A2)+...+P(An) In the exercise, it is given that Ω= {α,β} and ΣΩ={ Ø , Ω, {α}, {β} } It is…
therealbishop
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$X\sim\operatorname{Uniform}(0,1)$. Probability density function of $Y = X^3$

Suppose $X\sim\operatorname{Uniform}(0,1)$ and $Y = X^3$. What is the pdf for $Y$ ? Answer is given as: $$\frac{1}{3y^2}$$ But I get: $$\frac{1}{3\sqrt[3]{y}^2}$$
Jay P.
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What is the highest probability

At a faculty the probability of seeing a person greater than 190cm is 12%. From a class of $24$ people, is it more reliable to meet $2$ people above $190cm$ or $4$ people above $190cm$? I dont undersand. Consider that the solution may be related to…
Madrit Zhaku
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How to calculate marginal distribution of conditional distributions

So like let $Y | \mu \sim \operatorname{Poisson}(\mu $. $P(Y =y | \mu ) = \frac{e^{-\mu}\mu^y}{y!}$. Let $\mu \sim \Gamma(\alpha, \beta )$. I'm looking to find the marginal distribution of Y i.e. $P(Y = y)$ I don't have a textbook but found online…
ss sss
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Transformation of Random Variable $y=\arccos(x)$

Given random variable $x$, which has a bounded $\arcsin(a,b)$ distribution. I am trying to find the distribution $Y$ such that $y=\arccos(x)$. My intuition tells me that $Y$ is an uniform$(\arccos(a),\arccos(b))$ distribution. How do I go about…
moddinati
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How to read a probability distribution given as a matrix?

I'm currently reading up to try and complete an assignment but our lecture notes are very sparse and skip over the basics to instantly move onto solving random questions. Because of this I'm having trouble piecing together my understanding of…
Constantconfusion
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