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.

Filter by
Sorted by
Tagged with
0
votes
0answers
8 views

I am having trouble with this question

Suppose that we are attempting to locate a target in the three-dimentional space, and that the three coordinate errors (in meters) of the point chosen are independent normal random variables with mean ...
0
votes
3answers
47 views

Given $n=36$, $ p=20/36$, and $p_0=0.5$; calculate $p$-value

I know so far that: $H_0:\ p= 0.5,$ $H_1:\ p> 0.5.$ And that $z$-score: $0.672$ I did $1-0.44 = 0.56$ for $p$-value but got it wrong, the correct answer is $0.2514$
0
votes
0answers
8 views

Joint Distribution of a Time Series with lag = 2 ? Am I wrong or the book?

I try to reproduce the calculation of mutual information I(x;y) from the book "Nonlinear Analysis for Human Movement Variability" p319. Specifically calculating the joint distribution of the ...
1
vote
0answers
30 views

Probability on sex distribution

The problem comes from Feller's introduction to probability. The problem states: "Let the probability $p_n$ that a family has exactly $n$ children be $ap^n$ when $n \geq 1$, and $p_0 = 1 - ap(1+p+...
0
votes
0answers
7 views

Is this the correct way of solving probabilities in statistics?

Among the 30 applicants for a position at a bank, some are married and some are not, some have had experience in banking and some have not, with the exact breakdown being: ...
2
votes
1answer
13 views

Proving Expected Value Formula for Discrete Random Variable Involving Infinite Series

I am currently trying to prove the following formula. Let Y be a discrete random variable that assigns positive probabilities to only positive integers. Show that: $$ E(Y) = \sum_{k=1}^{\infty }P(Y \...
1
vote
1answer
19 views

Why is probability divided by time = annual rate? (Force of Mortality)

In force of mortality, one divides the probability of failure in a time interval $(x, x+\Delta x)$ by $\Delta x$. Apparently, this gives an annualised instantaneous rate of failure. In this article, a ...
0
votes
0answers
12 views

If $X_i$ follows $ U( \theta, \theta+1)$ and n is even. How do I find the probability distribution of median?

I have used the following transformation to find the joint pdf: $u= X_\frac{n}{2}$ and $ v = \frac{X_\frac{n}{2}+X_{\frac{n}{2}+1}}{2}$ The joint pdf I have found is like below: $f_{(U,V)}(u,v)= \...
0
votes
1answer
14 views

Probability of second ball being blue

There are $3$ boxes. One box has $2$ blue balls. One box has $2$ red. The last has one blue and one red. You randomly pick a box and take $1$ ball out. You see that it's blue. What is the probability ...
0
votes
1answer
33 views

100 Gambles of Roulette

I am stuck on the following problem: You go to Las Vegas with $\$1000$ and play roulette $100$ times by betting $\$10$ on red each time. Compute the probability of losing more than $\$100$. Hint: Each ...
0
votes
0answers
10 views

A practical question about probabilities and NS&I bonds investment

Here is a rather practical question, I and my son have different opinions about, please bear with me, it's a probability question: With NS&I bonds, is it better to buy many smaller value bonds or ...
0
votes
1answer
37 views

Flipping an unfair coin 5 times

I'm flipping an unfair coin 5 times. The probability of getting heads is $\frac{2}{3}$ and the probability of getting tails is $\frac{1}{3}$. What's the probability that at least 3 of the coins end up ...
1
vote
0answers
6 views

Explanation about finding the density with monotone supports and inverse transformation.

Let $X_1, X_2$ be random variables and $h(x_1,x_2)$ be a transformation that is monotone in $x_1$ for each $x_2$ on the joint support. Let $h^{-1}$ denote the marginal inverse transformation such that ...
0
votes
1answer
26 views

Probability Mass Function Understanding What To Look For!

Problem: For which value of $\alpha$ is the function $p_i=\frac{(\alpha+1)(i-\alpha)+2}{120}$ of $\{1,2,\cdots,10\}$ a p.m.f? My understanding is that $p_i=1$ and that $i=\{1,2,\cdots,10\}$, but ...
3
votes
0answers
46 views

Normal distribution and inflection points intuition

I was in class when my professor made a point that I had not seen before. He said to figure out (graphically) where the first standard deviation($\sigma$) in $N(0,\sigma^2)$ you can look at the point ...
4
votes
0answers
69 views

Conditions on angles between three points on a sphere (which are uniformly distributed)

Question: Let $A,B,C$ be three random, uniformly distributed, independent points on a sphere. What is the probability that none of these three points is at an angle superior than $\pi/2$ from the two ...
0
votes
2answers
38 views

Density of random variable max{ξ1, ξ2}

Let $\xi_1, \xi_2$ be independent and equally distributed absolutely continuous random variables with density $p$. How can I find the density of the random variable $\max(\xi_1, \xi_2)$.
2
votes
0answers
26 views

Probability of the last element being chosen is $b$

I have two elements: $a$ and $b$ Every step, I randomly choose one of these two elements to add to a box. Each element has a $1/2$ chance of being chosen. For example: Step 1: I choose $a$, the box ...
0
votes
0answers
13 views

Getting $P(Y=y)$ while having the cumulative distribution function graph without info about the $y$ axis

I am given the following graph: Question: Given the following graph of the cumulative distribution function of random variable $Y$. Calculate $P(Y=103)$ This type of question is usually easy, ...
2
votes
1answer
14 views

Probability of arrangement of letters following specific rules

I have letters ABCDEFG (7 letters). I want to find the probability that if I shuffle the letters and arrange them randomly that B is first and A is last (but I can pick any arbitrary two letters). I ...
0
votes
3answers
33 views

Fraction of probability terms

I repost the following question, since it has been deleted. Let $A$ and $B$ be independent events in a probability space which are each less than certain. Determine the value of the following ...
4
votes
3answers
236 views

if two computers are playing tic-tac-toe, but they are choosing their squares randomly, what is the chance for X to win?

I really have no Idea, but I would really like to know. I am good at math, but not that good.
31
votes
1answer
1k views

What are ways to compute polynomials that converge from above and below to a continuous and bounded function in $[0,1]$?

My interest is to take a coin of unknown bias $\lambda$ and use it to produce a coin of bias $f(\lambda)$. This is called the Bernoulli Factory problem, and only certain functions $f$ can be simulated ...
0
votes
3answers
36 views

Can I find a bound to show that $\lvert x-y\rvert ^{2}\geq c\lvert \lvert x\rvert ^2-\lvert y\rvert^2\rvert $

Can I find a constant $c$ to show that $\lvert x-y\rvert ^{2}\geq c\lvert \lvert x\rvert ^2-\lvert y\rvert^2\rvert $ for $x,y\in \mathbb R\; (*)$. Background to my question: In a proof I saw the use ...
42
votes
5answers
22k views

Precise definition of the support of a random variable

$\newcommand{\F}{\mathcal{F}} \newcommand{\powset}[1]{\mathcal{P}(#1)}$ I am reading lecture notes which contradict my understanding of random variables. Suppose we have a probability space $(\Omega, \...
0
votes
2answers
51 views

Are these two expressions the same?

Imagine that you have 4 sets, $A, B, C,$ and $D$. I was wondering if $$ (A \cap B) \cup \left[ (A \cup B) \cap (C \cup D) \right] \cup \left[ (A \cup B) \cap (C \cap D) \right] $$ is the same as $$ (...
0
votes
0answers
23 views

Adverse Drug Reaction Probability

I would like advice establishing how like to calculate a probability associated with an Adverse Drug Reaction. The assumptions are: • The period of research review is 1200 days. During the period of ...
2
votes
2answers
75 views

Balls and bins - average vs best case scenario

Assume we have $3$ bins: bins $L_1, L_2, L_3$, in each bin, there are $3$ balls. Alice is picking one ball from each bin at random. The balls can be either white or black. Alice does not know how many ...
1
vote
1answer
52 views

If I roll 20 six sided dice, what is the chance of there not being a 1?

Assume that the dice are fair. Wouldn't the answer be 5/6^20? I don't really know.
4
votes
1answer
49 views

What is the best book to learn probability theory through a linear algebra perspective?

I have heard from my linear algebra professor in undergraduate studies that probability theory can be examined using linear algebra. As a math student who enjoys linear algebra, does anyone have a ...
1
vote
1answer
21 views

Expected time in half-line for random walk

For a one-dimensional random walk (starting at $0$) for which we move $1$ unit to the right with probability $p$ and $1$ unit to the left with probability $q=1-p>p$, what is the expected time spent ...
0
votes
0answers
26 views

Analytical expression for the optimal trading fraction when returns are skew t distributed

Thorp's paper here details the derivation of a continuous approximation of the Kelly formula when returns are normally distributed. Let X be a random variable with $P(X = m + s) = P(X = m − s) = 0.5$. ...
0
votes
0answers
11 views

Which statistical dimension should I use as the conversion value for a sample of invoices with sample size of $210$?

I need to assign a conversion value for actions taken on a website. I have already processed the data for a sample size of $210$ paid invoices. The statistical analysis of the income values can be ...
0
votes
0answers
14 views

Binomial distribution but probability changes at a certain time

Consider a trial with success probability defined below. Let $0<p<q<1$. If it is $100,200,300$th trial, then the probability of success is $q$. If it is $400$th trial, then the probability ...
1
vote
1answer
19 views

Probability where there is dependent event

question: A lot contains $10$ items out of which $3$ items are defective. If three items are chosen at random without replacement find probability that only first one is defective? My approach: ...
0
votes
0answers
31 views

A version of the central limit theorem and probability inequality

Let $\{X_i\}_i^n$ be independent RVs with $E(X_i)=0$, $Var(X_i)=1$ and $S_n:=\sum_{i\neq j}^n c_{i,j}X_iX_j$ such that $Var(S_n)=1$ and obviously $E(S_n)=0$. It is now said that $$ P(|S_n|<\delta_n)...
0
votes
1answer
26 views

Probability of an Event A succeeding, if it constantly repeats another Event B when failing, which calls Event A on its' failiure

Essentially, I have events A and B. $P(A) = \frac{1}{2}$, and $P(B) =\frac{5}{9}$. Event A is called first, and if it fails, event B is called. If event B fails, event A is called again. How would I ...
0
votes
0answers
17 views

How to find the expected value before a bitarray is full?

If I have a bitarray of size $m$ with all $0$'s initially and one universal hash function $h: U \rightarrow [m]$ where each index in the bitarray has $\frac{1}{m}$ probability of being flipped to 1, ...
-2
votes
1answer
23 views

Drawing of balls without replacement

If there is urn filled with large number of balls , half the balls are white and half are red and a person takes out 4 balls , how much more likely is it to get 2 red ball and 2 white balls rather ...
1
vote
1answer
26 views

Inequality expectations

Suppose $X$ is a nonnegative random variable and $a$ and $b$ are nonnegative constants. I am trying to prove that $\begin{equation} \mathbb{E}[((a-X+b)^+-X)^+] \leq \mathbb{E}[((a-X)^++b-X)^+], \end{...
0
votes
0answers
25 views

Poisson alternatives

As a part of my Mathematics course, I am writing a paper on the probability of my favourite Youtuber's video uploads. I applied the Poisson distribution for the upload period of two years, where I ...
2
votes
1answer
44 views

Ace Of Spades and Two of Clubs Right After An Ace

I came across this question A Deck of 52 playing cards is shuffled and the cards are turned up and kept on the table. What is the probability that ace of spades and 2 of clubs come right after an ace?...
0
votes
1answer
25 views

What is the probability that someone has met a person with a disease given the number of diseased people

Let's say there's a group of 6000 people and each person knows other 10 people of that same group. 200 of these people tested positive for a disease, what are the odds for each person to have met at ...
1
vote
2answers
36 views

Confusion in one of the combinatorics/probability problem, with my approach for its solution.

The only contents of a container are 10 disks that are each numbered with a different positive integer from 1 through 10, inclusive. If 4 disks are to be selected one after the other, with each disk ...
1
vote
2answers
60 views

Let $A, B,C$ be subsets of $\{1,2,…n\}$. What is $P((A\cap B)\subseteq C)$?

My reckoning is that there are totally $2^{n} \cdot 2^{n} \cdot2^{n}$ options for $3$ subsets and for $(A\cap B)\subseteq C$ , for each of $\sum_{k=0}^{n}\binom{n}{k}$ options for C there are $\sum_{...
1
vote
1answer
26 views

Integral with respect to Probability Distribution

I want to integrate the following, but am not sure exactly how to do so. I'm working with a probability distribution $F(x)$ (i.e. $f(x)$ is a density function): $$\int_0^\infty \int_t ^\infty x^k dF(x)...
0
votes
1answer
32 views

Bayes' Theorem with 3 parameters

Can you please help me figure out how the following equation was derived using Bayes' Theorem? The left-hand side of the equation is the posterior distribution. $$f(x,y,z\mid D)=\frac{f(D\mid x,z)f(x\...
-1
votes
1answer
22 views

Solve for martingale progression in CRAPS

In craps the house has a 1.45% edge (51.45% chance to lose). If you martingale+1 (double up + 1 unit, every time you lose) and do this for 15 outcomes, then double up the initial bet for 30 more ...
1
vote
0answers
31 views

Monkey randomly typing on a typewriter with 26 letters problem proof using only Markov chain theory (without using Martingale theory)

There's a monkey randomly typing on a 26 letter keyboard, and the probability of each letter appearing is $\dfrac{1}{26}$. We need to find out the expected time until the monkey types a certain word. ...
1
vote
3answers
82 views

Two aspects of randomness

Consider a random sequence of integers 1, 4, 3, 8, 2, 5, 3, 8 ... The only sufficient condition for the sequence to be random is its unpredictability ie. probability of any number coming next ...

1
2 3 4 5
1741