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Questions tagged [probability]

For questions about probability. independence, total probability and conditional probability. For questions about the theoretical footing of probability use [tag:probability-theory]. For questions about specific probability distributions, use [tag:probability-distributions].

The probability that an event occurs is a number in the interval $[0, 1]$, which represents how likely the event is to happen. $0$ indicates it will never happen, $1$ indicates it will always happen.

For example, throwing two dice gives a total of $6$ five times out of thirty-six. We write $$P(X=6)=\frac{5}{36}$$.

Use this tag for basic questions about probability, independence, total probability and conditional probability.

For questions about the theory of probability, use instead. For questions about specific probability distributions, use .

105859 questions
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What does it mean for a random variable to "admit" a distribution?

Can someone explain the word "admit" and explain what would happen if it does not admit a distribution?
Project Backlog
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Probability of a Union

I know that $$P\left(\bigcup_{i=1}^{n} A_i \right)$$ is the sum of of the probabilities of all the sample points that are contained in at least one of the $A_{i}$'s. This is the probability of sample points belonging to exactly 1 event, exactly 2…
barry
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Coupon Collector Problem Extension

Humans have two copies of each of $23$ chromosome, for a total of $46$ chromosomes. If you want to sequence someone's DNA, you can just use a normal cell, since they have all the chromosomes. But if you have a sample of gamete cells, each one has…
Nishant
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Probability problem in networking.

Consider the following statement from Computer Networking A Top-Down Approach textbook, With packet switching, the probability that a user is active is $0.1$. If there are $35$ users, the probability that there are $11$ or more simultaneously…
user99297
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probability that the white balls are left in the urn

I don´t understand the solution of next problem: An urn contains n white balls and m black balls. The balls are withdrawn one at a time until only those of the same color are left. Show that with probability $$n\over m+n$$ they are all white The…
user128422
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Minimizing the variance of weighted sum of two random variables with respect to the weights

Suppose $X$ and $Y$ are two random variables. I would like to see if the solution to $$ \min_w \quad \mathrm{Var}(wX+(1-w)Y) $$ can be negative. I know that \begin{align*} &\mathrm{Var}(wX+(1-w)Y) \\ &= w^2 \mathrm{Var} X +…
Tim
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Proof of Double Expectation of a Conditional Expectation

There is a proof of $$ E(E(Y|x)) = E(Y) $$ $Proof:$ WLOG, suppose X and Y are two continuous random variables. Let $E(Y|x)=m(x) =\int_{-\infty}^{\infty} yf(y|x)\, dy$ Then $$ E(E(Y|x))=E(m(x))= \int_{-\infty}^{\infty} m(x) f(x) \, dx…
wanchihsin
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Show that $\max \left(\frac{|X_1|}{\sqrt{n}}, \dots, \frac{|X_n|}{\sqrt{n}}\right) \overset{d}{\to} 0, n \to \infty$

$X_1, X_2, \dots, X_n, \dots$ is a sequence of i.i.d random variables with $E[X_1] = 0$ and $E[X_1^2] = 1$. Show that $$ \max \left(\frac{|X_1|}{\sqrt{n}}, \dots, \frac{|X_n|}{\sqrt{n}}\right) \overset{d}{\to} 0, n \to \infty $$ I attempted to…
probability learner
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The probability of winning in a shootout, using a geometric random variable

Sir Lancelot and Sir Galahad are doing a shoot out, in which they try to shoot each other while shooting in the same time at each other. The probability of Sir Lancelot to hit Sir Galahad is 0.5 and the probability of Sir Galahad to hit Sir Lancelot…
user162354
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P(X > a) > P(Y>a) -- does it imply P(X>Y) > 1/2?

Given some real number $a$ can anyone prove that if $$ P(X > a) > P(Y > a) $$ is true then $$ P(X > Y) > \frac12 $$ is also true.
lowtech
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Drunken sailor's Random Walking

A drunken walker is on $x=0$, and if $x<0$, he falls and he dies.(Once he gets position $x<0$, he dies permanently.) There is $0
Maddy
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How to find the probability of truth?

A and B are independent witness in a case. The probablity that A speaks the truth is 'x' and that of B is 'y'.If A and B agree on a certain statement, how to find the probability that the statement is true ?
Quixotic
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What is the expected number of times to see k consecutive heads in n coin tosses?

For example, if k = 2, and you have the sequence HHH, then you've seen k consecutive heads twice.
gravitas
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Probability Of a 4 sided die

A fair $4$-sided die is rolled twice and we assume that all sixteen possible outcomes are equally likely. Let $X$ and $Y$ be the result of the $1^{\large\text{st}}$ and the $2^{\large\text{nd}}$ roll, respectively. We wish to determine the…
user158193
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This is question 3.3 from Alan Karr's Probability

What is the minimum number of points a sample space must contain in order that there exist $n$ independent events none of which has probability zero or one? I'm thinking the answer is $2^n$, but this is just from checking by hand for the values…
Pierre
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