Questions tagged [probability]

For basic questions about probability and the questions associated with the calculation of probability, expected value, variance, standard deviation, or similar statistical quantities. For questions about the theoretical footing of probability (especially using [tag:measure-theory]), ask under [tag:probability-theory] instead. For questions about specific probability distributions, use [tag:probability-distributions] instead.

93,374 questions
Filter by
Sorted by
Tagged with
61 views

Poor phrasing in probability problem, what is the problem even asking for?

If $m$ things are distributed among $a$ men and $b$ women, show that the chance that the number of things received by man is$${1\over2} {{(b + a)^m - (b - a)^m}\over{(b+a)^m}}.$$ I'm not asking for a ...
52 views

We have a density function: $p_{X,Y}(x,y)=ce^{-y}, 0\leq x<y<x+1$

$$p_{XY}(x, y)= ce^{-y},\quad 0\leq x \lt y\lt (x+1)$$ I need to find $c$. My try: $$\int_0^{\infty}\int_x^{x+1}ce^{-y}dydx = \int_0^{\infty}\int_0^{y}ce^{-y}dxdy = \ldots =1$$ Is the idea correct, ...
44 views

52 views

49 views

stop rolling dice until the cumulated sum is perfect square

You have a six-sided dice, and you will receive money that equals to sum of all the numbers you roll. After each roll, if the sum is a perfect square, the game ends and you lose all the money. If not, ...
58 views

What is the probability that EA > EC?

I found this question in one of my books: Square $ABCD$ has a length of $1$. Point $E$ is selected inside the square. Segment $EA$ represents the distance between point $E$ and one of the vertices of ...
30 views

Should I determine how long it takes to fix a problem or should I just fix it? [closed]

I was looking at the good-turing equation and was thinking about problem solving, and if: I should learn how long it takes to fix something or I should just fix it It has come up today in a ...
34 views

Integral bounds for $x\geq yz$

I am having trouble understanding the integral bounds. From what side should my understanding go (first or second?): first: as $z$ is between zero and one, $y$ is also between zero and one, thus $x$ ...
99 views

What is $\binom{n}{2} \binom{n}{1} + \binom{n}{3} \binom{n}{2} + \ldots + \binom{n}{n-1} \binom{n}{n-2} + \binom{n}{n} \binom{n}{n-1}$?

A bag contains $n$ white and $n$ black balls, all of equal size. Balls are drawn at random. Find the probability that there are both white and black balls in the draw and that the number of white ...
40 views

A soft question about the differene between guassian distribution and uniform distribution over a circle

Choosing $n$ independently and uniformly distributed points from a unit circle is relatively easy and there are many ways to do it. One way for instance is the rejection method; choosing points in the ...
42 views

Triple integral probability problem

We have density functions: $p_X = e^{-x}$ $p_Y = 2e^{-2y}$ $p_Z = 3e^{-3z}$ We need to find the density function of $p_{x+y+z}$. All three variables are independent. Because they are independent I ...
The time integration of Brownian motion is given by $X(t)=\int_0^tB(s)ds$. In order to show that $X(t)$ is a gaussian process I work with the definition that for any $t_0<t_1 < t_2<\ldots &... 0answers 18 views How do we name the X when we have an independent and identically distributed random variables X_1, X_2, ..., X_n? Also how to name data? I need to be sure about some jargon/naming. In this page we have "For i.i.d. random variables$X_1, X_2, ..., X_n$, the sample mean, denoted by$\bar{X}$, is defined as$\bar{X}=\frac{X_1 + X_2 + ...
Given a distribution $f$ of which i have already drawn $n$ random samples with real values, what is the probability of the next sample being in the top k of all samples? Edit: With the suggestion of ...