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 ...

learn more… | top users | synonyms (2)

1
vote
0answers
18 views

3 Events, Conditional Independence

Given $A,B,C$ such that: $$ P(A\mid B),P(A\mid B^c),P(B\mid C),P(B\mid C^c) \text{ are known } $$ and that $A,C$ are conditionally independent given $B$, so that: $$ P(A\mid B\cap C)=P(A\mid ...
0
votes
2answers
26 views

Games and statistics

Three individuals A, B and C alternate in contention of a game according to the following rules: A plays with B and the winner plays with C. The game continues until one of the individuals to win two ...
2
votes
2answers
41 views

How do mathematician make sense of “outcome” and “events” in probability?

One of the biggest challenge for me to understand probability is to make sense of this concept of outcomes and events. To put it plainly, it just doesn't feel like mathematics anymore when we talk ...
0
votes
1answer
298 views

partial differentiation of function of expectation of random variable

We have $E(U)=\int_0^B V f(V) dV + B \int_B^\infty f(V)dV$; Here $V$ is random variable. $E(U)$ stands for expectation of $U$. We have $Z=f(E(U))$ i.e. $Z$ is function of $E(U)$. Can we write ...
-1
votes
0answers
17 views

Is Grace's argument valid?

In this graph, Grace recorded in this table the favorite colour that her classmates like. Red: 6 Orange: 4 Yellow:10 Green: 3 Blue : 7 Grace used this data in the graph to make this argument: "Most ...
0
votes
2answers
14 views

Convergence Events with States

Ignatz repeatedly rolls a fair $6$-sided die. What is the probability that he rolls his first $5$ before he rolls his second (not necessarily distinct) even number? I don't know what to do about the ...
0
votes
3answers
44 views

Intuitive meaning of the probability density function at a point

I understand how to integrate probability density functions to find probability within a certain range. However, what I don't understand is what it would mean to set the variable (say x or y) to a ...
-2
votes
1answer
31 views

What time should Celia aim for in her sixth race to make the team?

To be on the 1-km race team, Celia must have a mean time less than 5 min 50 sec in her 6 tryout races. Her times in 5 races are: 6 min 2 sec, 5 min 53 sec, 5 min 45 sec, 6 min, and 5 min 34 sec. What ...
1
vote
1answer
304 views

Theater row brainteaser

I bumped into this brainteaser The Theater Row: Eight elegible bachelors and seven beautiful models happen randomly to have purchased single seats in the same 15-seat row of a theater. On the ...
1
vote
1answer
15 views

When randomly distributing n points amongst m people, what are the odds that one certain person will get a certain amount of points?

I'm mostly curious about how to find this in general, but the actual problem is with 20 points and 5 people. I know probability problems are very counterintuitive, and thus I was unsure after ...
0
votes
1answer
25 views

Probability with $n$ successes before $m$ failures

Independent trials resulting in a success with probability $p$ and a failure with probability $1 − p$ are performed. What is the probability that $n$ successes occur before $m$ failures? Given ...
0
votes
2answers
19 views

Mathematical Backing for Observations seen in Adding Independent Random Variables Together

So I have a function Y = F(N) that takes as an argument an integer number N and returns a summation of N sine-waves of different random parameters. I have plotted the results of two function calls ...
0
votes
2answers
27 views

defective component and probability

An electronics industry uses three plants from A, B and C in the ratio of $3$ to $2$ to $1$. However $1\%$ of components manufactured by A, $2\%$ of components manufactured by B and $3\%$ of ...
0
votes
0answers
15 views

Probability, expected frequency and resultant distribution skewed or not?

A population consisting of a certain proportion of defective items has mean $\mu = 2$. If a sample of 4 items is examined and repeated 200 times, obtain a) probability of an item being defective, ...
2
votes
1answer
43 views

Error in Billingsley?

Problem 8.25 in the third edition of Probability and Measure by Billingsley (1995, p. 142) is as follows: Suppose that an irreducible [Markov] chain of period $t>1$ has a stationary ...
7
votes
3answers
2k views

PDF of a sum of exponential random variables

Let $X_i$ for $i=1,2,...$ be a sequence of i.i.d exponential random variables with common parameter $\lambda$. Let $N$ be a geometric random variable with parameter $p$ that is independent of the ...
0
votes
1answer
46 views

Probability that AJ is guilty

A crime has been committed by a solitary individual, who left some DNA at the scene of the crime. Forensic scientists who studied the recovered DNA noted that only five strands could be identified and ...
2
votes
2answers
327 views

Probability of winning blackjack dice game?

I know a little bit about probability but I am not sure how to calculate this: In a dice game of blackjack, there are two parties. The player and the dealer. The aim of this game is to get as ...
1
vote
1answer
20 views

Finding conditional probability using Baytes formula

Suppose that chips for an integrated circuit are tested and that the probability that they are detected if they are defective is $0.95$, and the probability that they are declared sound if in fact ...
0
votes
0answers
12 views

Coupon collector problem with $k$ distinct coupon sets to complete

In the standard coupon collector problem we have an urn with $n$ different coupons, from which coupons are being collected, equally likely, with replacement. Simple analysis shows that the expected ...
3
votes
2answers
34 views

Selecting k distinct numbers from an array with increasing probability distribution

I have to select k distinct numbers from an array such that probability of a number getting selected is more if it is at the end of the array (probability increases linearly). I'm thinking of ...
1
vote
1answer
207 views

Conditional expectation of the maximum of two independent uniform random variables given one of them

Given $X_1$ and $X_2$ two independent random variables both uniformly distributed on $[0,1]$. What is the conditional expectation of $\max\{X_1,X_2\}$ given $X_2$? And the conditional expectation of ...
1
vote
0answers
11 views

Maximum difference between tails in absolute value

I toss a fair coin $n$ times. Some notation: $S_i=$ difference between #heads and #number of tails after the first $i$ tosses, $1\leq i\leq n$. $M_n=max(S_1,S_2,\dots,S_n)$, ...
0
votes
0answers
5 views

Concentration bounds on Pearson correlation matrix

I am interested in (rather sharp if not the finest) tail/concentration bounds for the Pearson correlation matrix: let $X_1,\ldots,X_N \sim \mathcal{N}(0,1)$ be correlated random variables; let ...
1
vote
2answers
36 views

Probability that among 3 random digits two different one

I have been trying to solve the following problem: What is the probability that among 3 random digits, there appear exactly 2 different ones? The formula for no repititions is: ...
1
vote
3answers
39 views

Adding two random variables with convolution

I am trying to understand the purpose of convolution of two probability functions. Also when it is appropriate to use the convolve function on two independent probability distributions. ...
3
votes
3answers
894 views

Expressing “Probability that #successes is an even number” mathematically

Needing a little help with my probability concept. Here's the question: An urn contains $10$ red balls, $20$ green balls and $30$ blue balls. Each trial consists of drawing a ball from the urn ...
1
vote
1answer
43 views

Age distribution when meeting

I have a question regarding Poisson process. I will tell the story in the context of a player-monster game. Consider a player who is born at $t=0$. He will win the game if he can survive until ...
0
votes
1answer
25 views

uniform distribution vs normal distribution for discount use case [on hold]

Problem statement: Reward a customer with lucky draw coupon of X% discount in between 1% to 100% Assume that slabs are pre-defined ( all are theoretical) 1% discount : 90% customers 10% ...
0
votes
2answers
25 views

Simplifying with Summation

This is a problem out of my statistics book but my issue is simplifying from Step 3 to Step 4 below: Step 1: var X=$\sum\:p_i\:(x_i-E[X])^2$ Step 2: var X=$\sum\:p_i[x_i^2+E[X]^2-2x_iE[X]]$ Step ...
0
votes
2answers
39 views

Two urns, A and B, each with two drawers.

If you have two urns, A and B, each with two drawers. The urn A has a gold coin in a drawer and a silver coin in the other drawer while the urn B has a gold coin in each drawer. An urn is chosen at ...
1
vote
1answer
29 views

Chessboard pawns arrangement clarification

I have a 8 X 8 chessboard, and 8 identical pawns. These pawns are arranged at random. What is the probability that the pawns are arranged in such a way that each row and column have only one pawn? My ...
3
votes
0answers
35 views

rolling a single die ten times

I have the following problem on a homework assignment for my Probability theory course: You roll a single six sided die ten times. What is the probability that you roll four 1's, three 2's, and three ...
2
votes
2answers
128 views

Expected number of tosses for a number to repeat $N$ times given an $n$-sided die.

I am currently reading a "pop-science" book on statistical fallacies. On page 36 the authors discuss how events can cluster around certain locations by chance. The authors exemplify this by a $6*6$ ...
0
votes
0answers
26 views

Conditional distribution

One point is chosen at random in the square $Q=\{|x| + |y| \leq 1\}$. Let $(X, Y)$ coordinates that point. a) The random variable $X$ and $Y$ are independent ? b) Find the density of $X$ given that ...
0
votes
2answers
28 views

Understanding the geometric distribution

Simple question that has to do with the interpretation of the geometric distribution and frequency function: $P (X=k) = (1-p)^{k-1}p $ for $k = 1,2,3... $ where we are interpreting X as being up to ...
0
votes
1answer
41 views

Rumor and probability

31 people in a community, a person has a rumor to a second which, in turn, repeats to the third, etc. At each step the person receiving the rumor is randomly chosen among 30 people available. a) Find ...
3
votes
1answer
28 views

Expected value of trials to obtain a red ball in a box of white balls.

I have a problem that involves a box containg N balls, one of which is red and the rest of which (N-1) are white. The question involves finding the expected value and variance for the number of trials ...
-1
votes
1answer
55 views

How many steps would it take to get to the top of this staircase?

There are 26 steps in a staircase. You have a 51% chance to step onto the next step, and a 49% chance to step back down to the step prior. Assuming you are already on the first step, how many steps ...
0
votes
2answers
41 views

How might I use this function to determine probability?

I am trying to make a random number generator that is sorta special. Basically it generates a number between 5, and 17. The twist that I need math help on is that I want to have a variable "P" that ...
0
votes
3answers
27 views

Dice roll - Geometric Distribution Question

I am having a hard time understanding the concept of a negative binomial distribution. For example the question: How many times do you expect to roll a six-sided die before landing on the number ...
2
votes
1answer
75 views

Packing of discrete random variables with finite second moment

I am considering a discrete random variable $X \in\mathbb{R}$ with $N$ points (where each point has non-zero probability) and $E[X^2]=1$ and $E[X]=0$. Let $d_l$ be the the smallest distance between ...
2
votes
3answers
101 views

Probability that the eventually a six on a dice will appear.

Dave rolls a fair six-sided die until a six appears for the first time. Independently, Linda rolls a fair six-sided die until a six appears for the first time. Let $ m$ and $ n$ be relatively prime ...
1
vote
0answers
25 views

Combining a set of conditional probabilities

I'm interested in combining a set of conditional probabilities into one. For example, if I know the following probabilities: P(illness|male) ...
1
vote
0answers
26 views

Uniformly boundedness of convolutions

Assume $X$ is an absolutely continuous random variable with pdf $f:\mathbb{R}\to[0,\infty)$. Assume further there exists $M>0$ s.t. $|f(t)|\leq M \quad\forall t\in\mathbb{R}$. Let $X_1,\dots,X_n$ ...
-1
votes
2answers
33 views

Deal 4 cards from a deck of 52 cards. What is the probability that we get at least one card that is diamonds?

Deal 4 cards from a deck of 52 cards. What is the probability that we get at least one card that is diamonds?
-2
votes
0answers
18 views

How to transform 3 probability values to a specific range?

There are 3 probabilities say x, y and z such that x+y+z = 1. Now, we need to convert these three probabilities together in the range of 0 to 1. If x is 1 then it should be 0, if y is 1 then it should ...
3
votes
1answer
19 views

Almost sure convergence through subsequences

$\{X_i\}$'s are independent Poisson random variables with parameters $\lambda_i$ respectively satisfying $\sum_{n=1}^{\infty}\lambda_n=\infty$. Define $S_n=X_1+X_2+\cdots +X_n$ then show that ...
0
votes
2answers
40 views

What is the distribution of a binomial variable where the number of trials is itself random?

We do the following experiment: Select a random element $k$ from $\{1,\dots,n\}$. Toss $k$ fair coins. Define $X$ = the number of heads. What is the distribution of $X$? Given $k$, the variable ...
2
votes
2answers
28 views

characteristic function implies degenerate distribution

Let $X$ be a random variable with characteristic function $\phi(t)$ satisfying $|\phi(t)|=1$ for all $|t|\leq 1/T$ with some $T>0$. Show that $X$ is degenerate. i.e there is $c$ such that ...