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)

3
votes
1answer
451 views

Poisson Processes and Arrival of Passengers at a bus stop

Arrivals of passengers at a bus stop form a poisson process $X = {X(t); t>= 0}$ with the rate of 4 per unit of time. Assume that $T$ denotes the arrival time of the next bus. Then $X(T)$ is the ...
1
vote
1answer
17 views

Drawing cards that satisfy multiple conditions

I'm looking to determine the odds of drawing a certain number of cards from a given deck, where the cards drawn must include several different types. For example, a deck of 27 playing cards contains ...
1
vote
1answer
640 views

Conditional expectation of an exponential random variable

Let $X$ be an exponential random variable with rate $\lambda$ Use the identity below to solve for $E[X|X < c]$ $$E[X] = E[X|X < c]*P(X < c) + E[X|X > c]*P(X > c)$$ So right off the ...
1
vote
1answer
212 views

Real life scenario, probability model required for accidental vs supernatural causation.

A = HUMAN 1 B = HUMAN 2 A is related to B, specifically A is the father of B A goes on holiday 5 years ago, staying in a hotel in popular tourist spot near Scotland (long way from home) During ...
0
votes
2answers
60 views

Cumulative distribution function of Y1 and Y2

Given scenario: Jim invites two friends J and W to a party. The arrival times of the two friends are independent and each is uniformly distributed over an hour starting from 19:00. Define the ...
0
votes
2answers
391 views

a red and green die are rolled. what is the % of getting a sum of 6 given that the green die is odd

The answer that the teacher gave us for this problem is 1/6 but I'm having a hard time getting there. This is what I did. The chance of getting an odd in the green die is 3/6 or 1/2. If the green ...
2
votes
2answers
72 views

Poisson distribution proof question

I'm reading over the Poisson distribution proof and trying to understand how $$\frac{n(n-1)\cdots(n-k+1)}{(n-\lambda)(n-\lambda)\cdots(n-\lambda)}$$ tends to 1 as $$n\rightarrow\infty\text{ ?}$$ ...
1
vote
1answer
29 views

Calculate a probability involving drawings from bivariate normal variables with Xi and Yi i.i.d

There's a question which has been troubling me along with my earlier post. To be honest, I'm not entirely sure on how to proceed. All I know is that if X~N(mu,sigma^2) then P(X < A) = P(Z< ...
41
votes
1answer
1k views

How likely is it not to be anyone's best friend?

A teenage acquaintance of mine lamented: Every one of my friends is better friends with somebody else. Thanks to my knowledge of mathematics I could inform her that she's not alone and ...
1
vote
1answer
163 views

Expectation of (1/x)-1 possible transformation involved??

I'm a bit confused with the first steps in this problem: $F(x)=x^4$ for $0<x<1$ a) Find $E[(1/X)-1]$ b) Let $Y=(1/X)-1$. Find the support of $Y$, its pdf and CDF. Name its ...
3
votes
1answer
211 views

What is the value of this game?

We have 3 black and 2 red balls in an urn. If we pick a black ball, we lose 1 USD. If we pick a red ball we win 1 USD. We can chose to start the game or not. If we start the game we can stop after ...
0
votes
1answer
39 views

Probability of occurrence vs. Probability of x successes

I've been reading for two hours and I'm having a hard time getting the grasp of these two concepts. I'm developing a tool for a game, in which I'm given n dice and a success threshold (ie. roll at ...
0
votes
1answer
40 views

Convergence in Probability for a sequence

Given sample space $\Omega=[0,1]$ and P( ) the uniform probability measure define random variable $X_1,X_2,.....$ by $X_{2n}=\begin{cases} e^{2n} & \text{if $\omega\ \epsilon\ [0,\frac{1}{2n}]$} ...
0
votes
2answers
64 views

If $\mathbb P[X_n=k]=C_n\max(k,n-k)$ for $k=1,…n-1$, then find $C_n$

For an arbitrary $n\ge 3$, let $X_n$ be a random variable on $\{1,2,...,n-1\}$, whose distribution is $\mathbb P[X_n=k]=C_n\max(k,n-k)$ for $k=1,...n-1$ What is the value of constant ...
0
votes
1answer
18 views

$\tau_n = 2^{-n}(\lfloor2^n\tau\rfloor+1)$.$\tau$ is a stopping time.How to prove $\tau_n$ is a stopping time?

$\tau_n = 2^{-n}(\lfloor2^n\tau\rfloor+1)$.$\tau$ is a stopping time.How to prove $\tau_n$ is a stopping time? It is clear that $\tau$ is strictly less than $\tau_n$.But I just cannot show $\tau_n$ ...
1
vote
2answers
51 views

Random selection probability

Hello and thanks for looking at my question Im having trouble figuring out how to do this problem An urn contains ten numbered balls- four 1's three 2's two 3's and one 4 two balls are drawn ...
3
votes
2answers
62 views

Poisson distrubution proof question.

I was reading over the proof for the Poisson distribution and came across this sentence: "But since $$\left[1-\frac{\lambda}{n}\right]^n\rightarrow e^{-\lambda}$$ as $$n\rightarrow\infty$$, ..." Can ...
3
votes
4answers
7k views

Convolution of two Gaussians is a Gaussian

I know that the product of two Gaussians is a Gaussian, and I know that the convolution of two Gaussians is also a Gaussian. I guess I was just wondering if there's a proof out there to show that the ...
0
votes
1answer
145 views

Find $\operatorname E(X\mid Y)$ given that $X=U+V$ and $Y=UV$ when $U$ and $V$ are independent with exponential distribution.

I currently have a problem with a problem set I'm working. Suppose $U$ and $V$ are independent with exponential distribution with parameter $A$ ($T$ is exponentially distributed with parameter if ...
1
vote
2answers
81 views

Random selection of a committee

Hello and thanks for looking at my questions. I'm sure this is a very simple question but I just cant seem to understand it A committee of three is selected from a pool of five individuals : two ...
1
vote
1answer
70 views

Product of exponential distributions

Suppose $X_1$ is $\mathrm{Exp}(\lambda_1)$ and $X_2$ is $\mathrm{Exp}(\lambda_2)$. $X_1$ and $X_2$ are independent. Let $Y = \min (X_1, X_2)$ and $Z = \max (X_1, X_2)$ and $W = ZY$ . Compute the ...
1
vote
1answer
99 views

asymptotic normality and central limit theorem

Here's the question Can somebody explain the difference between asymptotic normality and central limit theorem? They seem very similar to me.
0
votes
3answers
61 views

Probability $X_1 + X_2+ X_3 \geq 1$

Let $X_1,X_2,X_3$ be independent random variables, each of which has the exponential distribution with parameter $\lambda=2$. Estimate the probability that $X_1+X_2+X_3 \geq1$. I have tried to ...
0
votes
1answer
39 views

Find the variance of X as a function of n.

For each integer $n≥0$, the function defined by $p(x)= (n+1)x^n $ if $0 < x < 1$ and $p(x)=0$ for all other x is the probability distribution function of some random variable $X$. Find the ...
0
votes
1answer
121 views

Smallest Possible Value of the Mean

Suppose that a and b are real numbers such that the function defined by p(x)=a+bx2 for 0≤x≤1 and p(x)=0 for all other x is the p.d.f. of some random variable Y. What is the smallest possible value of ...
1
vote
1answer
46 views

First Person out of 130?

Assume that the amount of time it takes for a student to finish a Math 425 midterm is a random variable with uniform distribution between 40 and 60 minutes. What is the probability that the first ...
0
votes
1answer
38 views

What is the probability that at least one of these three will function for at least 47 months?

A fictional company produces coffee makers. If T is the random variable representing the lifetime, in months, of one of these coffee makers, the probability density function p(x) of T is given by the ...
3
votes
1answer
73 views

Probability that the first person to be done with the test will leave after at most 41 minutes?

Assume that the amount of time it takes for a student to finish a Math 425 midterm is a random variable with uniform distribution between 40 and 60 minutes. Suppose that there are 130 people in the ...
1
vote
1answer
66 views

Probability and Intersections

I'm having trouble understanding the difference between conditional probability and dependent events. Even then, I'm not sure if that's what I'm having issues with. NB This is not a homework problem. ...
1
vote
1answer
40 views

What is the name of this sequence/progression?

Does the following sequence form some special sequence/progression (such as arithmetic progression, geometric progression, hypergeometric progression, and more): $$ p_k: = \frac{\lambda^k}{k!} ...
0
votes
3answers
74 views

How do i calculate probability of 6 numbers?

Hi all can anyone help me how to find probability of generating 6 different numbers from given 10 numbers?
0
votes
1answer
82 views

Conditional expectation of a stochastic process in filtered space

It was suggested* to me that if we have a stochastic process with independent increments, and $T > t$, then $$ E(X_{T-t}| \mathcal{F}_t) = X_{T-t} $$ where $\mathcal{F}_t$ is the filtration at time ...
0
votes
1answer
32 views

Probability of idenitical errors on a production line

(This is not homework, but rather a test study question that I'm stuck on) There are three production lines which, in total, produce 60 widgets in one shift. After a shift, it is found that 6 out of ...
0
votes
1answer
76 views

Expectation of the Product of a Poisson and an Exponential Random Variable

Problem: Consider a Poisson process with parameter $\lambda$ . Let $T$ be a random variable representing the time required to observe the first event, and $X_\frac{T}{K}:=N\left(\frac{T}{K}\right)$ be ...
0
votes
2answers
49 views

Probability that random variable is greather than a number

I'm currently writing my bachelor's thesis in game theory but am no that great at probability. I have a problem where I know the distribution of a random variable call it $X$ (a bunch of binomials ...
0
votes
2answers
54 views

Expectation of a function of two different transformations of a random variable

I have a random variable $X$ where the support of $X$ is non-negative and I want to compute the expectation of $aX\log(bX)$ where $a,b>0$ If I can chose how $X$ is distributed, is there a ...
0
votes
2answers
33 views

Solving for the Random Variable X in a Z score

I know I am going to hate myself when I find out the method of doing this is trivial. Anyways the problem is this. Let X be normally distributed with mean of 120 and standard deviation of 8. Find the ...
0
votes
1answer
116 views

Probability of a tetrahedron (die with 4 faces)?

I have been doing some questions from an exam review with no solution and I have no idea how to work this problem. I know that $Pr(A_1) = \frac{1}{2}$, $Pr(A_2) = \frac{1}{2}$, $Pr(A_3) = ...
4
votes
1answer
2k views

What are the exact odds of getting a perfect NCAA bracket?

With the NCAA March Madness Finals nearing, I thought it'd be appropriate to ask this. From everything that I've read and heard online, there seems to be varying opinions on the exact odds of getting ...
1
vote
1answer
106 views

Probability of binary-drawing-game for two players

Outline: 2 players Consecutive draws without putting anything back 5 total marbles 2 white, 3 black Given solution: -In the first game the white marble wins and for the person starting to draw ...
1
vote
2answers
56 views

Existence of a winning strategy against the probability of winning

Edit: I've made the question clearer. Suppose a game is played between $A$ and $B$, in which there exists a winning strategy for $A$. Suppose $A$ and $B$ play their moves at random, do we have ...
1
vote
1answer
30 views

$X$ and $X^2$ as discrete random variables

If $X$ is a discrete random variable with probability distribution $P(X = x)$, what does $X^2$ mean?
1
vote
2answers
69 views

Probability of sum over a window of binary vector

I have a vector of one's and zero's of length n with a probability p of observing a one and 1-p of observing a zero. I slide a (overlapping) window of size $k$ across this vector and take the sum ...
1
vote
0answers
19 views

Which parameters are used for MGF?

While finding the mgf of the binomial distribution we allow for the X to cover all values from 0 to N, the number we "choose". Why don't we have to cover all possible values for the p and q as well? ...
2
votes
1answer
46 views

n events of one process occuring before m events of another process

Assume that you have two independent Poisson processes, N1( t ) with rate λ1 and N2( t ) with rate λ2 . What is the probability that n events occur in the first process before m events occur in the ...
1
vote
3answers
846 views

Probability that one out of four players gets all four aces

What is the probability that exactly one player gets all four aces if a randomly shuffled deck is dealt to four players? My attempted working: ...
0
votes
1answer
22 views

Doubt in Scale Function

% speckle scale function Iuniform = imcrop(I,rect); q0_squared = (std(Iuniform(:))/mean(Iuniform(:)))^2; In the above equation, they are finding ...
0
votes
1answer
45 views

Conditional PDF of an order statistic

Let $Y_1,\ldots,Y_n$ (all scalars) be random draws from a common CDF $F$ that has a PDF $f$. As usual, $Y_{(r)}$ denotes the $r$-th order statistic (e.g. $Y_{(1)}$ is the smallest). Let $z$ be fixed ...
1
vote
1answer
20 views

Probability 3 events

Have a target that has 4 sections. Call them A, B, C, D. you throw there rocks one at a time, if they land outside the target or in a section that has aready got a rock in it you throw again without ...
0
votes
2answers
1k views

Four fair six-sided dice are rolled. What is the probability that at least three of the four dice show the same?

We can choose any value for the first one, so... $1 \times \frac{1}{6} \times \frac{1}{6} + (\frac{1}{6})^3$ will be equal to the answer. But this doesn't seem right to me.