# Tagged Questions

This tag is for basic questions about probability and for questions in which one wants to calculate a probability, expected value, variance, standard deviation, or similar quantity. For questions about the theoretical footing of probability (especially using measure theory), please ask under (...

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### Expected number of married couples chosen out of 50 different people

I've encountered this problem, and would like to know if my approach is right. We select 10 people out of a group of 25 married couples, what is the expected number of married couples chosen? ...
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### a collection of 20 marbles from infinite pool of 2 color marbles with replacement.. [closed]

I have an infinite supply of pink and blue marbles. Probability that any random draw will yield a pink marble is "p" and prob. of picking blue is 1-p. Let us assume p=0.4 if a numeric value helps. ...
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### Is there a faster way of computing the probability of a sum $S$ when $n$ dice are rolled? [duplicate]

So far, I've only had to deal with $2$ dice or $3$ dice problems. For example, if the problem asks to find the probability that a sum of $8$ will be achieved from rolling $3$ dice, I just list all the ...
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### Is it incorrect to call the probability mass function by the name “discrete probability density function”?

Commonly, the probability density function (pdf) is used when dealing with continuous random variables, while the probability mass function (pmf) is used for discrete random variables. This also ...
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### Switching independent experiments: Does $I_A(X_1,\dots,X_n,Y_{n+1},Y_{n+2},\dots)$ converge almost surely?

Suppose there is a sequence of independent random variables $X=(X_1,X_2,\dots)$ with $X_i$ taking values in some arbitrary measure space $E_i$. Now there is a second sequence $Y=(Y_1,Y_2,\dots)$ ...
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### How many possible solutions are there in 4 number game?

$4$ number game consist of $4$ random number from $0$ to $9$. The goal is to make the result equal to $24$. There are only operation four operation possible, addition, subtraction, multiplication, and ...
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### MLE of a distribution

I have a function $r=C(Q-Q^{1-\beta})$, where C and $\beta$ are constants. And I know the density function of Q. The density function of $Q$ is $\theta Q^{-1-\theta}$, where $\theta$ is a constant and ...
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### What is the expected number of samples you’ll take until $x_{i+1} > x_i$?

Randomly (but uniformly) sample a number between $0$ and $1$. Stop the first time that a sample is greater than the immediately previous sample. That is, if your samples are labeled $x_1, x_2$, etc., ...
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### chances of a group being all of the same sex [closed]

I was wondering, if there are 10 girls and 10 boys in a classroom, and they were randomly assigned in groups of four, what are the chances of there being a group with all people inside it the same sex ...
I want to prove that $Z_t$ the Doléans-Dade exponential is a local martingale i.e. that there exists a stopping time $\tau_n$ tending to infinity such that the stopping process \$\mathbb{1}_{\tau_n>...