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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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Probability Theory : convergence in distribution

I would need some help for a pratical exercise of probability about convergence of random variables. Consider the following distribution function : $F^{X_{n}}(x) = \frac{e^{nx}}{e^{nx}+1} ; n \geq 1$. Proof there is a sequence of random variables…
Hernium
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Letter Arrangements of M,A,R,Y

List all possible arrangements of the four letters m,a,r,and y. Let $\; C_1 \;$be the collection of the arrangements in which y is in the last position. Let $\; C_2\;$ be the collection of the arrangements in which m is the first position. Find the…
Jonarie Ramos Vergara
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Binomial distribution cdf as the number of trials tends to infinity

I am trying to establish the behavior of the cdf as the number of trials tend to infinity. With a certain probability of success and K number of successes, if we increase the number of trials to infinity, what would happen to the cdf plot. I have…
Waqas
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Probability Need help understanding how to work problem out

What number would complete this probability distribution? And could you explain how, I am new to this and my textbook isn't helping. x 3 7 11 P(X)0.38 0.29 ?
barb
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Creating random integers with distribution schema

I need to create an array that includes 0..5 integers. I'm able to create them randomly. But I need to create them according to below distributions. How can I get below distributions? Ps: I'm using numpy to create the array.
zontragon
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Finding the value of c for which two probabilities are equal

The amount of a certain chemical in a type $A$ cell is normally distributed with mean of $10$ and a standard deviation of $1$, while the amount in a type $B$ cell is normally distributed with a mean of $14$ and a standard deviation of $2$. To…
user170171
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Binomial Distribution Problem

Hello can someone please help me to answer this question it, it a binomial distribution question: An email message advertises the chance to win a prize if the reader follows a link to an online survey. The probability that a recipient of the email…
Nadun
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Trouble deriving sum of squared normals is Exponential with mean $2$

Box-Muller method hinges on the fact that $R = Z_1^2 + Z_2^2$ is Exponential with mean 2, where $Z_1, Z_2$ are independent standard normals. I want to derive this fact but am getting stuck. I proceed as follows: \begin{split} P(R = r) &=…
vdesai
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Random varible and dicrete probability distribution.

4 unbiased coins are tossed simultaneously. Obtain the probability distribution of the random variable 'numbers of head'.
Akshay
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Open-ended Bernoulli distribution

I've found myself puzzled by the following simple discrete distribution: open-ended Bernoulli distribution, which I will now define. The distribution has 2 parameters: $p$, the success probability, and $q$, the repeat probability. I will define it…
Bach
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Bounds on joint distribution

$X$ and $Y$ are distributed according to the joint PDF $$ f_{X,Y} (x,y) = \{ \begin{array}{lr} \frac{3}{7}x & : 1 \leq x \leq 2, 0 \leq y \leq x\\ 0 & : otherwise \end{array} $$ The random variable $Z$ is defined by $Z = Y…
Convergii
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Distribution of maximum run length of independent multinomial trials?

(I posted this on CV but I think here would be faster. After I get the answer, I will somehow merge two posts...) I am curious about the distribution of (maximum) run length given k independent trials when $p(X=1)=p_1, p(X=2)=p_2, ...,…
KH Kim
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$n$ books and 3 friends expected value of $X$ = no. weeks all friends read the same book

There are 3 friends each with $n$ books, each friend has a set of their own $n$ same books, each one takes a random permutation of the $n$ books. They all read one book every week (n consecutive weeks). Now, we let $X$= no. of weeks they all read…
user168915
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Probability density functions of multiple random variables

Problem: Two birds have landed on a power line that spans the 100' distance between utility poles. a) What is the average distance between the birds? b) The line runs north and south. Another bird lands on the line. What is the expected position of…
Bill Jenkins
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Joint probability density function wherein two random variables are uniformly distributed on a quarter-circle

Random variables, X and Y, are uniformly distributed in the quarter circle, with center at the origin and a radius of one in the first quadrant of the x,y plane. Please find the joint PDF of X and Y. Attempt at Solution: I've worked a problem…
Swamp G
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