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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171 views

a question on Stochastic Calculus

I encounterred a question on Stochastic Calculus as following, but I don't understand the meaning of $\mathcal{N}$ here, can any expert explain me a little bit? Thank you very much in advance! ...
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0answers
43 views

How to calculate P(W|F) empirically?

So say I have three files $(A, B,C)$ that are filled with words. Say for a specific word $W_{i i}$ want to determine the probability of the word given a file. that is Calculate: $$ ...
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9answers
13k views

Why is the expected value $E(X^2) \neq E(X)^2$?

I wish to use the Computational formula of the variance to calculate the variance of a normal-distributed function. For this, I need the expected value of $X$ as well as the one of $X^2$. Intuitively, ...
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2answers
309 views

Drawing three balls from an urn with ten balls

An urn contains four white balls and six black. Three balls are drawn with replacement. Let $x$ be the number of white balls. Calcaulate $E (x)$, $VAR(x)$ and $\sigma x$. I don't know how to ...
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1answer
85 views

Question Related to Multinomial Expansion

A probability question I was trying to solve the other reduced to this simple statement: Find the coefficient of $x^{21}$ in the expansion of: $$(1+x+x^2+x^3+x^4+x^5)^6$$ Obviously, I can get a ...
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1answer
114 views

Confidence Intervals Paradox

Say I have two independent random variables, $X$ and $Y$. If I give you a 90% confidence interval on each $(x_1,x_2)$ and $(y_1,y_2)$, i.e. $P(X\in(x_1,x_2))=.9$ and $P(Y\in(y_1,y_2))=.9$. If I asked ...
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1answer
64 views

Probability of a new number given a set of $n$ previous numbers?

I have a set of numbers (each one corresponding to a payment made from the same person) and I would like to assign a probability value to a new specified number given that historical data. I've ...
2
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2answers
49 views

Probability of $a>cb$, $a$ and $b$ are uniform in some ranges.

What is the probability $P(a>cb)$ where $a$ and $b$ are drawn uniformly & independently in some ranges, for example, $a$ in $(0,1)$, $b$ in $(0,n)$? $c$ is some constant and $c>0$.
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1answer
84 views

When deriving the multivariate normal distribution, please explain this limit

In deriving first the bivariate case, I have come across this limit that confuses me, (7). It should be easy enough for a mathematically mature person to understand and explain. Is the limit a typo? ...
4
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2answers
106 views

Unimodality and continuity for probability distribution

From Wikipedia about the conditions for the Vysochanskij–Petunin inequality The sole restriction on the distribution is that it be unimodal and have finite variance. (This implies that it is a ...
2
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0answers
128 views

Derivative of measure-valued function

I have a measure $\mu^x$ which is the law of a random variable and depends on $x$. The specific situation I am thinking of is $\mu^x$ is the law of $X_t$, the solution of an SDE with $X_0=x$. If I ...
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1answer
306 views

How to calculate accuracy of the sample approximate of expected value

I have independent random values $x_1 < ... < x_n$ with the same distribution function. I want to find expected value of this distribution by my . Of course it will be $X = \frac{1}{n} \sum_i ...
4
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1answer
94 views

Compression of equations and coincidence?

I stumbled across an interesting paper last night. Basically, it tries to see if mathematical equations have meaning by determining how well they "compress" the results. For instance, he says the ...
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1answer
419 views

Conditional Poisson process

I am having difficulty with the following problem: A store promises to give a small gift to every thirteenth customer to arrive. If the arrivals of customers form a Poisson process with rate ...
0
votes
1answer
601 views

Marginal PDF from a joint PDF with an integral that does not converge

I have a joint PDF that has gone through some transformations of $f(x,y) = 12x\displaystyle\frac{1-y}{y^3}$,$0<x<y^2$, $0<y<1$ It definitely is a valid PDF as it has a double ...
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1answer
79 views

test for sigma finiteness

A measure $\mu$ on (E,$M$) is $\sigma$-finite if and only if there exists a strictly positive function $f$ in M such that $\mu f<∞$ . Please help me out with the proof. Thank you.
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2answers
722 views

How to compute this integral involving a cdf?

$\int_0^\infty\Phi(\frac{-x}{\sqrt{2}})d\Phi(x)=?$ where $\Phi(x)$ is the cumulative distribution function of a standard normal random variable.
5
votes
1answer
193 views

$X$, $Y$ gaussian variables, $\mathbb{E}[X^2Y]$ and $\mathbb{E}[X^3Y]$ as a function of its means, variances and covariance?

Let be X and Y two not independent Gaussian random variables of means $\mu_X$, $\mu_Y$ and variances $\sigma_X$, $\sigma_Y$, respectively. Let also be $\Sigma$ the covariance between X and Y. I'd ...
2
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2answers
280 views

Probability question (CDF , PDF etc) [duplicate]

Possible Duplicate: Please correct my answer (Probability) I have to calculate the density function of the random variable $Y= 1-X^2$, given that: $f(x) = \frac{1}{9}(x+1)^2$, where $-1 ...
2
votes
1answer
185 views

Gaussian Mean Width

Consider $K\subset S^{n-1}$. Its Gaussian Mean Width is defined to be $$ \mathbb{E}\,\sup_{x\in K}\vert \big<g, x\big>\vert $$ where $g$ is a standard Gaussian Random Vector in ...
2
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3answers
94 views

How come the probability here is not $1/({_{13}C_3})$?

Here's my question. I have $6$ gold coins, $4$ silver coins and $3$ bronze coins in my pocket. I take out three coins at random. What is the probability that they are all of different material? I ...
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0answers
128 views

Decomposing Characteristic Functions of Infinitely Divisible using Levy-Khintchine Representation

Consider an infinitely divisible random variable X defined on $\mathbb{R}$ with Levy triple $(a,\sigma,\nu)$ following from the LK representation. Can all or any infinitely divisible random ...
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1answer
91 views

Cumulative probability and predicted take in a raffle?

Not sure if this is the right term! If I have a raffle with 100 tickets in at $5 each, and people pull a ticket sequentially, how do I calculate the likely return before the winning ticket is drawn? ...
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0answers
167 views

Composition of multi complex gaussian normal distribution

assume $w_0$, $w_1$, $w_2$, $w_3$ are circular symmetric complex Gaussian distributions, and the composite of $$ h = e^{j\theta_0}w_0 + e^{j\theta_3}w_3 - e^{j\theta_1}w_1 -e^{j\theta_2}w_2 $$ so ...
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1answer
160 views

Please correct my answer (Probability)

I have a probability issue that i am dealing with now. Maybe you could help me a bit :-) . I have to calculate the density function of the random variable $Y= 1-X^2$, given that: $f(x) = ...
1
vote
1answer
323 views

Probability and distribution function

Can some one please tell me how to do it? Let $(i,j)$ denote the numbers on the top faces when a pair of fair dice is rolled. Let $X(i,j)=i+j-3$. Find the range of $X$. Find the probability ...
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0answers
92 views

How to calculate the new conditional probability in a baseyan network when an evidence on one attribute is provided?

I'm trying to understand bayesan networks also I created a simple bayesan network according to same sample date. This is the network (created with Hugin Lite) There is one class (Failure) and two ...
4
votes
3answers
226 views

Probability of Random number selection

Suppose you are asked to pick any random real number. Then you have a choice to pick any number between -∞ and +∞, i.e, infinite numbers. The probability that you select a particular number n = 1/∞ = ...
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votes
2answers
656 views

Lottery “Sum” forecasting

I was wondering if anyone can provide some mathematical insights to forecasting the "SUM" in this link as a time series. It is an oscillatory, range bound and poisson distribution. How can Monte Carlo ...
0
votes
1answer
101 views

What is the chance of repeating a combination of random image sets within 20 images over 100 trials?

Title states an example, I'll give the general case question then repeat an example. I have N images and plan to randomly pick k of the possible N images into a set. The order does not matter. I ...
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1answer
268 views

Probability puzzle with balls in an urn

I need help with a problem about classic probability and possible extensions to it. Suppose you have an urn with $N$ distinguishable balls. Every time you draw $k$ balls out of $N$. Some possible ...
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2answers
938 views

Circular Permutation Problem

We play Russian Roulette. There are 4 blanks 2 bullets (assuming you randomly pick 2 places the bullets can go in the cycle, then spin it randomizing the how the rotation ends up). If someone ...
4
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1answer
303 views

Given n raffles, what is the chance of winning k in a row?

I was reading this interesting article about the probability of of tossing heads k times in a row out of n tosses. The final result was $$P = 1-\frac{\operatorname{fib}_k(n+2)}{2^n}\;,$$ where ...
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2answers
110 views

Finding the domain and distribution of $Y = X^3 + 6$ for $X \sim U[-2,2]$

A small probability problem that I am struggling with... Let $X \sim U[-2 , 2]$. Find the distribution of $Y = X^3 + 6$. My main problem is the domain of $Y$. I found that the domain of $Y$ is ...
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2answers
322 views

Why is this term required for a probability about drawing cards from a deck

Five cards are drawn from a standard deck (not replaced). Determine the probability of drawing exactly 3 hearts and 2 diamonds. The expression for the probability is: ...
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1answer
706 views

Box with N two-color balls, randomly chosen, with and without returning

Suppose there is a box with $N$ balls, $k$ white and $N-k$ black. If after choosing a ball it gets returned to the box, then: $$p(\text{white})=\frac{k}{N},\space\space\space p(\text{black}) = ...
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1answer
90 views

A statistics and probability problem

Assume that the average reaction time of drivers is normally distributed with average of 1.1 s and a standard deviation of 0.3 s. Compute the probability that in the selected simple random sample of ...
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3answers
177 views

Erdős Probabilistic method

My question is based on the Erdos probabilistic method. I am trying to read from the paper here. The proof of Theorem 1 contains the statement Since a block sequence is monochromatic with ...
5
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1answer
161 views

Clarification: Viewing $\mathbb{R}^n$ as a probabilistic state space

In this MathOverflow post on visualizing high-dimensional spaces, Terry Tao states that "the fact that most of the mass of a unit ball in high dimensions lurks near the boundary of the ball can be ...
0
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1answer
41 views

Computing a single probability out of a joint probability

Given the joint probability and the factored term: $$ P(S,T,G,F,B) = P(G|B,F) \cdot P(S|T,F) \cdot P(T|B) \cdot P(B) \cdot P(F) $$ I want to compute $P(S = s)$, thus I want to compute ...
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2answers
93 views

Computing conditional probability out of joint probability

If I have given a complete table for the joint probability $$P(A,B,C,D,E)$$ how can I compute an arbitrary conditional probability out of it, for instance: $$P(A|B)$$
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3answers
503 views

What is the proper way to compare discrete set of data to a continuous probability distribution?

I have a set of data points that I an trying to approximate with a few different probability distributions such as the gaussian or student t distributions to see which fits best. The first step to ...
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2answers
55 views

The distribution for one of the components of a minimized sum?

I have a complicated thing I would like to find the distribution for. Let's say I have a random variable $X\sim F_X(x)$ supported over $(0,1)$. I have two independent draws from $F_X$, which are ...
1
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1answer
523 views

How would one rescale the variance and standard deviation of a set of data?

I have a set of data with a certain mean, variance, and standard deviation. I centered the mean around the origin the standard way by subtracting it from the data. Now how do I modify the data to ...
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1answer
125 views

Can I average c.d.f's for the average of draws from different distributions?

Let's say I have 3 random variables, $X$, $Y$, $Z$ with c.d.f.'s $F_X(x)$, $F_Y(y)$, and $F_Z(z)$. All are supported over $(0,1)$ I want to define $Z$ such that $Z = aX + (1-a)Y$ (i.e. a weighted ...
3
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2answers
122 views

Is this number random?

I'm trying to create a random 6 digit code. If I generate a random number between 0 and 999999 and then pad it with zeros to make it 6 digits is it random or is it biased in some way? E.g It ...
2
votes
1answer
634 views

Expected Value of the Difference between 2 Dice

What is the expected value of the absolute difference between 2 N faced dice? What about the difference between 2 dice one with N faces and one with M faces? While finding the expected value ...
0
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1answer
946 views

Coin flipping games - dependent trials

I'm still trying to learn probability and in furtherance of this I have posed myself two questions about coin flipping series. I don't know how to answer these questions because these aren't ...
2
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3answers
568 views

Modified two child problem. Find the probability that both are girls, given that at least one is a girl born in March.

A family has two children. Assume that birth month is independent of gender, with boys and girls equally likely and all months equally likely, and assume that the elder child’s characteristics are ...
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1answer
278 views

Probability question autocorrelation function

Let $V_1$,$V_2$, $r$ be independent random variables, where $V_1$, $V_2$ are Gausian with the same distribution and $r$ is uniformly distributed in $[0,1]$ if $$X(t)=V_2 I(r \geqslant t)+V_1 ...