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 ...

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18 views

Probability of a five-card poker hand contains cards of five different kinds and does not contain a flush or a straight?

Important Information There are 13 kinds of card in poker and 4 distinct suits for each kind of card. A Flush is 5 cards of the same suit in one hand A straight is a hand with 5 cards of ...
3
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1answer
43 views

Where do I go wrong?

Suppose $X,Y$ are independent Uniform$(0,1)$ random variables. Find the probability $P(Y\geq X\mid Y\geq\dfrac{1}{2})$. Please note that I know the correct answer and that I have arrived at the ...
0
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1answer
19 views

Probability, Minmize Gaussian distribution

There is a one problem that bugs me a while: Two random variables with distribution $X$ is $\mathrm{Gaussian}(\mu=\frac{-3}{\sqrt5}, \mathrm{var}=\frac 9 5)$, and $Y$ is ...
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0answers
10 views

conditional dependence and sum of random variables

I know that $Y \perp\!\!\!\perp (X,Z)|A \Rightarrow Y \perp\!\!\!\perp X|A$, but is the following true? 1) $Y \perp\!\!\!\perp (X+Z)|A \Rightarrow Y \perp\!\!\!\perp X|A$ I feel like the addition ...
1
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1answer
13 views

Two dice are thrown

A die is numbered in such a way that its faces show the number 1, 2, 2, 3, 3, 6. It is thrown two times and the total score in two throws is noted. Complete the following table which gives a few ...
-1
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0answers
22 views

$P(X|Z,Y)\not = P(X|Z)$ if and only if $P(Y|Z,X)\not = P(Y|Z)$ [duplicate]

So suppose we have $$P(X\mid Z,Y) = \frac{P(X,Z,Y)}{P(Z,Y)}$$ and $$P(Y\mid Z,X) = \frac{P(X,Y,Z)}{P(Z,X)}$$ How can we show that $P(X\mid Z,Y)\not = P(X\mid Z)$ if and only if $P(Y\mid Z,X)\not = ...
2
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0answers
62 views

If $X_1,X_2,X$ are iid random variables with $X_1+X_2$ has the distribution of $aX$, find all characteristic functions of $X$.

If $X_1,X_2,X$ are iid random variables with $X_1+X_2$ have the same distribution as $aX$ for some real $a$, what are the possible characteristic functions of $X$? Let $\varphi_X(t)$ be ...
1
vote
1answer
14 views

How to write this conditional probability equation?

Question is Alice tosses a fair coin, then rolls a fair die. If the result is <=2, she tosses fair coin ,otherwise she tosses an unfair coin(80% gets head). .what is the probability that she gets ...
0
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0answers
17 views

The probability of rolling a 12, another 12, and then an 11

So, two fair dice are rolled in Monopoly. If you roll doubles, you get two roll again. If you get doubles a third time, you go to jail. I am trying to calculate the probability of rolling a 12, a 12, ...
1
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2answers
33 views

Stopping time intuition

Let $(X_n)_{n \geq 1}$ be independent and identically distributed random variables with $P(X_n=1)=P(X_n=-1)=\frac {1}{2}$ for all $n \geq 1$ and let $S_n = X_1+X_2+ \cdots +X_n$. If we define a ...
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0answers
17 views

Solving a Uniform Probability Distribution

I was wondering about the following question. Let X be the point chosen on a line segment of length one splitting it into 2 segments. Find the probability the the shorter segment contains ...
-1
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0answers
5 views

Assume that we have assessed probability distributions for two discrete uncertain quantities [closed]

Assume that we have assessed probability distributions for two discrete uncertain quantities: Variable 1 and Variable 2, and that they are probabilistically dependent (mutually relevant). How many of ...
2
votes
0answers
39 views

Show that a measure is a probability measure

I have trouble with this question: We define an arc segment $B(\theta, \eta, r, R)=\{x \in \mathbb{R}^2\vert \omega(x)\in [\theta,\eta], \Vert x \Vert_2 \in [r,R] \}$ where $0 \leq \theta \leq \eta ...
0
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1answer
19 views

brownian motion scaling

I have the following probability : $P( W(t) > 0 \mbox{ and }W(2t) > 0)$ on some textbook it is claimed that this is equal to $P( W(1) > 0 \mbox{ and }W(2) > 0)$ due to the scaling ...
0
votes
1answer
41 views

Probability of getting the correct direction, given you get the same answer

A town is composed of $2/5$ out of town couples and $3/5$ in town couples. If a couple is from out of town, the probability that the husband and wife will give you the correct directions ...
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0answers
20 views

If there is a 10% chance of me winning a tennis match… [closed]

If there is a 10% chance of me winning a tennis match, what would the chance be of me winning 1 match if I played 10 matches?
1
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1answer
30 views

Computing the expected value of the product of two discrete variables

I didn't know why I compute $E(XY)$ wrongly. $$X=(1, 2, 0.5, -1),\qquad Y=(-2, 1, -0.5, 2).$$ $$E(XY) = \frac{-2 + 2 -0.25 -2}{4} = -0.5625\text{ (incorrect)}$$ because ...
0
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0answers
19 views

Doob's decomposition of $X_n=\sum _{m=1}^n1_{B_m}$, where $B_m \in \mathcal{F}_m$.

$X_n=\sum _{m=1}^n1_{B_m}$, where $B_m \in \mathcal{F}_m$. I want to find the Doob's decomposition. I think $X_n=Y_n+Z_n$, where $Y_n$ is a martingale, $Z_n$ is a predicable process. Then ...
0
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1answer
28 views

Poisson process at infinity

Is the following probability well-defined? How do I deal with the fact that the time is infinite and the number of arrivals if infinite (N)?
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1answer
35 views

Probability puzzle : Expected no. of coins in the smaller pot

There are two pots of coins having size m & n. A new coin is thrown and goes to 1st pot with probability m/(m+n) and to 2nd pot with probability n/(m+n). We start with both pots of size 1 & 1 ...
0
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1answer
25 views

Probabilty of 2 buses or more arriving at a bus s top at the same time

I do have a basic understanding of laws of probability, but need assistance with figuring out this question This is a general question that applies to all bus stops- As you know the length of red ...
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0answers
15 views

Poisson Distribution finding $E(x^4)$ [closed]

Given $E(x^n) = E((x+1)^{n+1})$ with mean $=1$. Thanks
4
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2answers
64 views

What is the expected value of $\min\{|X|,|Y|\}/\max\{|X|,|Y|\}$ assuming $X$ and $Y$ are independent?

So I need to compute $$E\left[\frac{\min\{|X|,|Y|\}}{\max\{|X|,|Y|\}}\right]$$ given $X,Y \sim$ Normal$(0,1)$ and independent. What I am having trouble seeing is whether $\min\{|X|,|Y|\}$ and ...
1
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3answers
39 views

What is the probability that a fair coin comes up tail three out of four flips?

As the question asks, what is the probability that a fair coin comes up tail three out of four flips? I know the probability of getting tails on one flip is 1/2, but I'm not sure how to solve this for ...
0
votes
1answer
29 views

Can I calculate this probability?

I need some help with a small probability question someone asked at work: I have 3 random variables: $B, A, L$. $A$ and $L$ are independent, and I need to calculate: $$ P(B|A,L) $$ But I only know ...
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1answer
26 views

Understanding steady state distribution

I need some help verifying that my understanding of steady state distribution is indeed correct. I have a transition diagram (model). With around 100 states and 6 variables. I have used a software ...
1
vote
1answer
30 views

Expected waiting time for bus

Suppose that the inter-arrival time between consecutive buses is 15 minutes with probability 0.5 and 30 minutes with probability 0.5. You just arrived at a bus stop. What is your expected waiting ...
0
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0answers
25 views

Probability considering history

Is it possible to calculate the probability of a number being chosen considering the number of total elements, the number of elements to be selected and how many times this element has already been ...
2
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0answers
27 views

relationship between the probability of sum of iid random variable and the probability of one random variable

I have $n$ iid random variables $ X_i $, which satisfy $ X_i>0$. I want to know the relationship between the following two probabilities, $$\mathbb{P}\left(\sum_{i=1}^{n}X_i > z \right) \qquad ...
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1answer
32 views

Probability : Maximize the expected payoff

Given $2$ random variables $X, Y$ that take integer values with uniform distribution from $0$ to $100$. You play a game in which a random value of $x$ comes first & you have to decide if the ...
1
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1answer
23 views

Find $\mathbb{P}(X > t+h \mid X>h)$. [closed]

Random variable has a probability distribution with density: $g(x)=xe^{-x}\mathbf{1}_{x \geq 0}$. Find $\mathbb{P}(X > t+h \mid X>h)$.
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0answers
17 views

Limiting Gumbel Form

Given a set of values $x_1 > x_2 > ...$, which represent existing observed order statistics from a large sample drawn from a distribution $F$ with the upper tail in the Gumbel domain of ...
0
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1answer
22 views

Select K numbers from N numbers fairly

I want to fairly select K numbers out of an array of N number. I know that this problem can be solved using Reservoir Sampling but I want to know if this approach is correct too? ...
1
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1answer
24 views

A question about the Integral geometry and geometric probability.

In the book: Integral Geometry and Geometric Probability, (p16-17), the author proved that the measure of randomly throwing three points P1, P2, and P3 on the plane such that the circumdisk and the ...
1
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1answer
22 views

probability of waiting time, chosen a random sample

The amount of time that a customer spends waiting in a counter is a random variable X with mean 8.2 minutes and SD = 1.5 minutes. A random sample of n = 81 customers is observed. Find the probability ...
1
vote
1answer
33 views

Comparing Sample Mean and a Random Variable

Let $X_{(i)} = ( i = 1,2, \ldots, n+1)$ be a random sample of size $n+1$ that is produced from a normal population. Let $M$ be the sample mean of the first $n$ random variables in this random sample. ...
5
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1answer
56 views

What are some good references on how probability theory got mathematically rigorous?

I am working on a term paper for an analysis course and I thought it would be interesting to talk about the connection between analysis and probability theory. Honestly, it would also benefit me a lot ...
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1answer
26 views

Can someone please show the steps from the question to the answer?

I have a question which has an answer without steps in between. Can someone help? $$m(t)=E\left(e^{tY}\right) = \sum_{y=0}^n \binom{n}{y}\left(pe^t\right)^yq^{n-y} = \left(pe^t+q\right)^n$$ To not ...
1
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2answers
43 views

Proof of Law of Total Probability

Two players take turns flipping, independently, a fair coin, where first player starts. Game ends as second heads comes up. The player who flips the second heads wins the game. Define the event: A = ...
1
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1answer
19 views

What can you say about two independent events A and B in a Sample space S

If we assume that A and B are disjoint example P(A∩B) = 0, what can I say about P(A) and P(B)
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2answers
28 views

Probability that this stamp is one that you haven't seen before

Suppose you have 4 stamps with probabilities 0.2, 0.4, 0.3, and 0.1, respectively. Each time you pick a stamp is independent of every other pick. Suppose you pick your 10th stamp. What is the ...
0
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0answers
21 views

Determine how closely one set matches another. [closed]

I am looking for ways to determine how closely one set matches another set. I'm devising a way to infer consumer preference for a business, but I have lots of ways I can tweak my model. My model will ...
1
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1answer
22 views

Expected score in marksmanship competition.

Problem: Marksmanship competition at a certain level requires each contestant to take ten shots with each of two different handguns. Final scores are computed by taking a weighted average of 4 times ...
0
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1answer
38 views

Randomly picking pedestrians to figure out where to go in the city

$2/5$ of couples are from out-of-town (oot), while $3/5$ of couples are from town. If a couple is from oot, the probability the husband and wife will give correct directions independently is $3/4$. If ...
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2answers
22 views

Generating a new password using each of (A-E) and (0-9) only one time randomly

Suppose you generate a password by randomly mixing 5 letters (A-E) and 10 numbers (0-9) in any order without replacement, producing a 15 character password. If all distinct passwords are equally ...
1
vote
1answer
36 views

Show $P(X|Z_1,…,Z_n,Y)\not = P(X|Z_1,…,Z_n) \Leftrightarrow P(Y|Z_1,…,Z_n,X)\not = P(Y|Z_1,…Z_n)$

If we have two random variables $X,Y$ and a set of random variables $\{Z_1,...,Z_n\}$, are there any common proofs of the result in the title? Which theorems does this follow after?
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0answers
29 views

Is there a better way to mathematically use this data than the way I am doing it?

I am trying to use math to predict NFL fantasy football scores. My current process for projecting a players score is as follows: For every team (32 teams), I list the average points it gives up to ...
0
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0answers
21 views

Poisson Distribution: Trouble understanding this example [closed]

first time posting on this stack exchange, could you please help me with this question, I haven't covered Poisson distribution in a while and I am struggling to answer this: The number of code ...
2
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1answer
28 views

what is a formula for working out dice chance percentages?

I am not a student or a maths type person. Instead I play a lot of board games and one in particular. Arkham Horror / Eldritch Horror. It uses a dice system to calculate successful rolls and I would ...
2
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2answers
59 views

A difficult probability question about choosing seats

I am bad at probability questions, help please.