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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6 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
20 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
29 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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0answers
31 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
35 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 ...
-1
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0answers
42 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
17 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
15 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
13 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
29 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 ...
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2answers
18 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 ...
1
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1answer
17 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 ...
1
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1answer
18 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
32 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 ...
6
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0answers
46 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
14 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
votes
1answer
39 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 ...
0
votes
1answer
28 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
votes
1answer
25 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 ...
-2
votes
2answers
41 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 ...
1
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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
9 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
11 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
46 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
10 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
29 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 ...
1
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1answer
21 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
14 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
15 views

Help me understand how finding related distributions work

$$G(a)=\frac{6400}{a^2}$$ So this is the question, and I know well to answer any type of question like this. Here's how I do? (i) $$F(t)=\int_{1/2}^{T} \frac {1}{2t^3} dt = ...
1
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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
18 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 ...
0
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1answer
23 views

Bounding the difference of random variables by coupling.

Suppose we have two probability densities differing by atmost $\delta$. Is it possible to use coupling to have two random variables with the above two densities differing by less than $\delta$? I ...
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0answers
14 views

Standard deviation of absolute distance of a 1D random walk

Given a 1D random walk (simple +1, -1 movements from the axis) I've seen proofs that the expected absolute distance tends to Sqrt(2*n/PI) and I've plotted graphs of 1D random walks along with this ...
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2answers
23 views

Probability Puzzle: Exactly one of two specific balls among $N$ balls in $n$ draws.

We have an urn with $N$ different balls of all colours, including one white and one red ball. We draw $n$ times without replacement. After $n$ iterations, what is the probability that among the ...
0
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2answers
36 views

What is the probability that I will get the same permutation when shuffling a deck of 52 cards? [duplicate]

I am doing a research paper about this topic. It has really puzzled me and although I seem to have found a way to calculate it, my answers are rather weird. I assumed that since 1300 AD a total of ...
1
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1answer
28 views

How many will not be selected in repeated tries?

Suppose I have $25$ uniquely identifiable objects, i.e., I know which is which once it has been selected (but they are not distinguishable in the selection process). I select $5$ objects at random, ...
0
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0answers
19 views

Find $E[Z_1 | aZ_1 + bZ_2]$

Let's $Z_1,Z_2$ be a random variable such that $EZ_1^2 < \infty$ and $EZ_2^2 < \infty$. Find $E[Z_1 | aZ_1 + bZ_2]$ where $a,b \in \mathbb{R}$. We don't know what is distribution of $Z_1$ and ...
0
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1answer
34 views

Conditional probability problem and Alias Method

I hopefully someone can help me with this problem of conditional probability: "A disk server receives requests from many client machines and requires 10 milliseconds to respond to each request. The ...
0
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2answers
15 views

Let Y be a random variable denoting the age at which a piece of equipment fails…

Let Y be a random variable denoting the age at which a piece of equipment fails. In reliability theory, the probability that an item fails at time y given that it has survived until time y is called ...
0
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1answer
18 views

Chance of winning in a raffle

A raffle consists of 10 sheets with 10 numbers (1 to 10) on each sheet i.e. 100 chances in total. The draw is done by first selecting a sheet at random and then selecting the winning number out of the ...
2
votes
4answers
78 views

Time-based probability question

Two adult male baboons are introduced to the same $50$ ft. square cage. Male A looks at Male B for a total of $5$ hours in the first ($24$ hour) day, and Male B looks at Male A for a total of $3$ ...
0
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1answer
18 views

A Question on the Scaling Invariance of Brownian Motion

I read the following paragraph. Let $B_t, \ t \in [0, \infty)$ be a standard linear Brownian motion. For each $q > 4$, define the following sequence of sets. $$ \Omega_k := \left\{\omega \in ...
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0answers
13 views

Probability of Multiple Hits in Blackjack

In a 6 deck Blackjack game, what is the probability of a player hitting 4 times and still having a hand total of 20 or less, allowing for the option to draw a 7th card? What is formula to find this?
2
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0answers
26 views

how to related a weakly convergent random variable with its k-th moment

Let $\{X_n\}$ be independent random sequence with zero mean and unit variance. Suppose $$S_n:=\sum_{m=1}^n \frac{X_m}{\sqrt{n}} \Rightarrow X\sim \mathcal{N}(0,1)$$ holds. (Here "$\Rightarrow$" ...
1
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1answer
22 views

Simple bounding question for an expectation with truncating function

Let $\{X_m\}$ be independent random sequence. I want to show the following result Given $E[X_m^2]:=\sigma^2 < \infty$ and $$0 = \mathop {\sup }\limits_m P\left( {\left| {{X_m}} \right| > ...
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0answers
34 views

necessary conditions for these conditionals to be consistent with some joint distribution

Let $A$, $B$, and $C$ be random variables taking discrete values in the set $\{0,1\}$. I'm trying to find necessary conditions such that the conditional distributions $$X\mid Y,\,Y\mid Z,\,Z\mid X$$ ...
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1answer
46 views

Requesting deeper understanding of binomial coefficient

I noticed that $\binom {52} 4$ * $\binom {48} 1$ is $5$ times that of $\binom {52} 5$. So for example, if we were to draw $4$ cards from a standard deck then draw $1$ more, we cannot just say there ...
2
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3answers
35 views

Confidence Interval has no relation to the probability?

An Intro to Stats class has the following problem: Find and interpret the 90% confidence interval for the true mean The provided answer is this: ...
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0answers
14 views

How to show that a set of random strings has unit probability

I am encountering a problem where I want to show that the generation of a random string terminates in finite time with probability one, where the termination is condition is reaching an element of a ...