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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Transition probability of Brownian Bridge

This is homework so no answers please Consider Gaussian $X_i\sim N(0,t_{i}(1-t_{i}))$ s.t. $\frac{X_{1}}{(1-t_{1})}$ and $\frac{X_{2}}{(1-t_{2})}-\frac{X_{1}}{(1-t_{1})}$ are independent (with ...
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0answers
11 views

Probability of upper quartile student

A teacher was asked by her principal to select 7 students at random from her class to take a standardized math test, which will be used to determine how well students at that school are doing with ...
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1answer
12 views

Possible/Impossible Probability Question

I'm not sure if there is a question like this already here, but... I just thought of a question related to probability, and I was wondering if it was possible: Suppose you want to ask someone to ...
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1answer
22 views

probability of teacher selecting students

A teacher was asked by her principal to select 6 students at random from her class to help out on an outing to a senior's home. In her class, she has 6 girls and 4 boys. The principal believes that ...
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0answers
8 views

Expectation under different probability measure

For two different probabilities, if they are equivalent, then does there exist a r. v such that the signs of its expectation under those two probabilities are different?
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1answer
28 views

A gambler who is equally likely to either win or lose one unit

A gambler who is equally likely to either win or lose one unit on each gamble will be down n before being up 1 with probability 1/(n + 1); or equivalently, P(gambler is up 1 before being down n) = ...
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0answers
18 views

Estimate on the Positive probability of not hitting finite measure sets in $\mathbb{R}^{d}$

In $d\geq 3$, we have that BM is transient a.s. i.e. $\lim_{t\to \infty}|B_t|=\infty$. But does this imply $1-P_x(T_A<\infty)>0$ for Borel sets $A\subset \mathbb{R}^d$ with ...
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5answers
39 views

Expectation of two dice game

The game plays like this: You roll two dices at the same time. If you get same number on both dices, you have to roll again, until you get different numbers. If you get different numbers, you stop. ...
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1answer
14 views

In Texas Hold'em poker, is the ranking according to chance of beating 1 opponent's hand the same as according to beating multiple opponents?

So in Hold'em poker you can rank hands according to the probability of beating one randomly generated opponent's hand. However no one can compute the exact probabilities of beating 8 random opponents' ...
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1answer
8 views

Bernoulli trials case in probability

A fair die is tossed twice. About how many times would you expect to roll 3 or greater? So based on sequence of Bernoulli trials: P(exactly k successes in n trials) = C(n,k) p^k q^(n-k) where p = ...
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0answers
21 views

probability distribution function of two independent variables

Let $X$ be a random variable whose distribution function is $F_X(t)=3^{-t}$. Suppose that $Y$ is another random variable whose distribution function is $F_Y(t)=4^{-t}$. What is the probability that at ...
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3answers
31 views

Expected number of rolls on a dice?

You roll a die until you have seen a 5 on 4 of the rolls (e.g. ⟨5,3,2,5,4,1,6,5,2,5⟩. What is the expected number of rolls this will take? I think that I am way overthinking how I should be going ...
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1answer
12 views

Covariance matrix of Y when we have the covariance matrix of X

If the random vector $\mathbf{X}$ is transformed according to \begin{align*} Y_1 &= X_1\\ Y_2 &= X_1 + X_2 \end{align*} and has a covariance matrix $$ \mathbf{C}_X = ...
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1answer
15 views

Solving inhomogenous first order difference equation (recurrence relation)

I have the equation (arising in a probabilistic context) $$ x_n = a(1-x_{n-1}) + (1-a)x_{n-1} $$ and I'm told that there is a solution of the form $c_1 + c_{2}\lambda^n$. How do I solve it, i.e. how ...
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0answers
17 views

Likelihood interval

Assume that $Y_1, Y_2, \ldots , Y_n$ are independent Poisson random variables each with rate parameter $\lambda$. Assume $n$ is sufficiently large enough so that the central limit theorem (CLT) ...
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1answer
28 views

Statistics: Simple pick from bag problem

I am doing a personal project with neural networks and want to see how accurate the predictions are compared to just plain old guessing. I'm sure this is a typical probability textbook problem, but I ...
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0answers
6 views

How to generate a random vector with a triangular autocorrelation

I am trying to generate N random vectors that when correlated with themselves converge to a triangular function. The approaches I have been trying to follow are reversing a PCA procedure ...
2
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0answers
16 views

Approximation of minimum among many binomials

We choose $k$ numbers independently from the binomial distribution $B(n,1/2)$, where we can think of $n$ as large. What is the expectation of the minimum of the $k$ numbers? Is there a good way to ...
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0answers
13 views

Is this application of the law of total probability correct?

Let us consider a counting process $N(t)_{t\geq0}$ which is neither Markovian nor Levy. Is it correct to write $$ \mathbb{P}(N(t)=j)=\int_{0}^{t}\mathbb{P}(N(t)=j, N(s)=i)ds $$ for $j\geq 1$ and ...
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0answers
10 views

What is the definiton for “best probability measure”?

I'm looking for this definition is notes that use the phrase and elsewhere, but it just isn't there. Does anyone else recognize the phrase?
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2answers
28 views

Finding the total permutations of the cards in the hand.

There are $36$ unique cards containing $9$ ranks ($1$-$9$) of $4$ suits (diamonds, hearts, clubs, and spades). A hand is a collection of $9$ cards. The hand must contain all $4$ of the $1$s (one from ...
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1answer
40 views

The probability that $3$ random points on the circumference form a right-angled triangle?

In my probability theory course, I dealt with a similar problem which asks for the probability that $3$ random points on the circumference of a circle lie on the same semi-circle. But it makes me ...
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1answer
34 views

Help with Probability

Hey Im a new guy here and need some help. I have an assignment bugging me. I can't really figure out which why to go around it. I'm thinking conditional probaility but how to apply the Bayes Theorem ...
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0answers
40 views

Checking my solution for a probability question? [on hold]

Hi, I have unfortunately lost my solutions. I got (i) which is 9!, but there are no answers for the second question. I stated that P(none together)=1-P(3 together)-P(2 together) and got the ...
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2answers
60 views

Number of ways to seat people around a circular table

I got (i) which is $9!$, but there are no answers for the second question. I stated that $$P(\text{none together})=1-P(\text{3 together})-P(\text{2 together})$$ and got the answer $7/12$. Is this ...
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1answer
20 views

what do these odds ratios represent?

I am reading this article in which is given the matrix of the joint probabilities of two random variables, X=$(x_1,x_2)$ and Y=$(y_1,y_2)$. Let's say they are $(p_{1,1},p_{1,2},p_{2,1},p_{2,2})$. ...
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2answers
17 views

is it true that conditional expectation Y to X is a function of X?

I mean, is it true that $E(Y|X) = \phi(X)?$ if so, how should we derive the form of X?
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0answers
17 views

Accelerometer data integration (MMSE)

Based on the raw accelerometer measurements use simple integration on the raw $X$ and $Y$ axis data to determine the velocity and position. If we assume a linear model $Y = aX + b$ for determine the ...
1
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2answers
36 views

Integral of pdf

I need to find the integral for this pdf but I don't know if I need to, or can, take the integral of two variables at the same time. $$ f(x;\theta)=\frac{x}{\theta^2} e^{-x^2/(2\theta^2)} ,\quad ...
0
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2answers
20 views

Probability of two points being part of two segments of different size

This may be an easy question but my probability skills are a bit rusty since I haven't used them for while. Say that we have a line with ten consecutive points. We are to choose two segments out of ...
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1answer
23 views

Expectation over 2 random variables, help needed

Hi I am new here and I hope I can get some help. My question is about taking expectation over random variables. Lets say I have two random variables $\Xi$ and $\theta$ where $\Xi$ is for example a ...
3
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1answer
33 views

Bayes' Net Conditional Probability

I have a Bayes' Net with 4 boolean nodes connected in a diamond shape. I want to find the probability of one of the middle nodes being true given that the ones above and below are both true. So ...
2
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2answers
39 views

Probability of 8 or 9 digit sequence colliding in the same place in two 65 digit numbers

I have two numbers: 3032643431333337636238613038343231383364303731376566303037663231 3861663464383131656131653461343961343364303737663565356561653361 36430373 ...
7
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1answer
72 views

seems easy set problem

let A B C be three finite set, prove that: $$|A\cap B|/|A \cup B| + |B\cap C|/|B \cup C| - |A\cap C|/|A \cup C| \le 1$$ It seem's simple, but I tried it for a long time and cannot get it out. Maybe I ...
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0answers
17 views

Urn problem (possibly a coupon collectors problem)

In an urn with 10 different coloured balls (each colour has an equal chance to be selected, let's say m balls of each colour). Can I find the mean number of draws to : Have one colour from 10 ...
0
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1answer
49 views

In frequentism, does every event have a probability?

For an infinitely repeatable trial with event space $\Omega$, and an event $A\subseteq \Omega$, the frequentist probability of $A$ is defined: $P(A):= \lim_{n\rightarrow\infty} \frac{n_a}{n}$, where ...
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1answer
29 views

Probability function of X and Y when two balls are drawn with no replacement

Two balls are drawn at random from a box containing ten balls numbered 0, 1, ... , 9. Let random variable X be the larger of the numbers on the two balls and random variable Y be their total. ...
0
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1answer
27 views

The best way to graph a lot of data

I have a lot of feature vectors in the form of: v1=[x0, x1, x2, x3, x4] where x0, x1, and x2 can take binary values. either 0 or 1 x3 and x4 can take values from 0 up to 9 I have a lot of vectors ...
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2answers
43 views

What is the probability that two five card hands have the same pair? [on hold]

Two players both are dealt five cards from a standard well shuffled 52-card deck. a) What is the probability that both hands contain same pair? b) What is the probability that both hands contain same ...
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2answers
21 views

Find the distribution function for Y for the following density function

I am to find the distribution function for Y given the following density function $$f(y)=\begin{cases} y,\quad 0<y<1\\ 2-y, \quad 1 \leq y < 2\\ 0, \quad\text{elsewhere}\\ \end{cases}$$ So ...
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0answers
10 views

Matching Gamma Statistics with Poison Statistics

Confidence intervals with Poisson distribution would be greatly helped by matching an equivalent gamma distribution. Can someone lay out how to match a Gamma Distribution to a poisson distribution? ...
0
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1answer
12 views

Probability of non repeated value in a set of vectors (with integer values) for any number in the same vector position.

Suppose a set with $m$ vectors ($m$ finite) defined by $V_{i} = (x_{vi1},x_{vi2},\dots,x_{vin})$, with $i \in \left\{1, 2, \dots, m \right\}$ and $2 \leq n \leq p$, for a given $p \in \mathbb{Z}$ ...
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2answers
48 views

Probability Question A fair coin is tossed repeatedly until a head appears

Can you help me with this. A fair coin is tossed repeatedly until a head appears. Let $N$ be the number of trials until the rst head appears. Then a fair die is rolled $N$ times. Let $X$ be the ...
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0answers
13 views

Dependent Bernoulli trials when probability of success depends on last failure

Assume you have a series of $n$ Bernoulli trials $B_1,\ldots, B_n$ each with unconditional probability $p_i$, and these are dependent in the following way: $$\mathcal P(B_i=1 | \mathcal F_{i-1}) ...
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2answers
30 views

Optimal Number of White Balls

There are C containers, B black balls and infinite number of white balls. Each container should have at least one ball. Each of the containers may contain any number of black and white balls. Action ...
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1answer
23 views

Maximum of Correlated random variables

I am trying to find the CDF $Z = \max(X_1,X_2,\dots,X_N)$ and in my case $X_i$ are correlated. Is there any transfer domain or one to one function where I can derive the CDF and invert back to current ...
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0answers
15 views

Probability exercise easy [on hold]

Angelo X distribution normal (1000,400) and Bruno Y distribution normal (1400;300). Which is the probability P(X>Y)?
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0answers
17 views

How to solve using Jacobian?

I am looking for a way to find the joint pdf of vector $Z=[Z_1,Z_2,Z_3,Z_4]$ where $Z_1= a_1 X_1^2 + a_2X_1Y_1+ a_3 X_1Y_2 + a_4Y_1^2 + a_5Y_2^2$ $Z_2= b_1 X_1^2 + b_2X_1Y_1+ b_3 X_1Y_2 + b_4Y_1^2 + ...
1
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1answer
26 views

Paley Wiener stochastic integral

Sorry for the stupid question, no answers necessary anymore! let $(B_t)_{t\in [0,1]}$ be a standard Brownian motion and $F\in C[0,1]$ differentiable. Then the sequence (which is an easy version of ...
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0answers
23 views

A reference for a Gaussian inequality ($\mathbb{E} \max_i X_i$)

I am looking for a reference to cite, for the following "folklore" asymptotic behaviour of the maximum of $n$ independent Gaussian real-valued random variables $X_1,\dots, X_n\sim ...