# Tagged Questions

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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### Calculate the probability in winning tennis game.

A tennis tournament has $2n$ participants, $n$ Swedes and $n$ Norwegians. First, $n$ people are chosen at random from the $2n$ (with no regard to nationality) and then paired randomly with the ...
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### Expectation of the fill distance of $N$ random points in $[0,1]^s$

Let $x_1,\ldots,x_N$ be uniformly distributed points in $[0,1]^s, s \in \mathbb{N}$. What can be said about $$\mathbb{E} \left(\sup_{x \in [0,1]^s} \min_{i \in \{1,..N\}} \|x - x_i\|_2 \right)$$ ...
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### Probability Average amount of rolls

I have a question regarding probability. I'll start by saying I've never taken a statistics or other similar course and was trying to work out this for a game. On average how many attempts will it ...
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### Random walk with drift

Let $X_1,X_2,...$ be independent and identically distributed $\mathbb{Z}-$valued bounded random variables with mean $a=\mathbf{E}[X_1]$, and let $S_n = X_1+\cdots+ X_n$ be the associated random walk. ...
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### Expected value of the exponential of a Geometric Brownian motion

I am trying to compute the following expectation: $$E[ \exp (A_T)],$$ where $A_T = - C \int_{0}^{T} \exp( 2 \alpha W_t - \alpha^2 t) dt$, with $C$ and $\alpha$ positive constants, $W_t$ a standard ...
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### Why the probability is $0$ but possible

We want to take a random number from natural numbers how much is the probability that,the number be $1$? When we want to say the probability we say it is $0$ but we say zero for impossible things but ...
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### Forecasting Query on probabilities

many Thanks if you can help with this query. Player A and Player B are due to play a darts match. Player A has a record of scoring between 80 and 140 in each of his last 35 rounds of throws. Best ...
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### Stats question bionomial distribution. [closed]

It is known that 47% of students at a large university are male. If we take a random sample of 200 students at the university, what is the approximate probability that less than half of them are male? ...
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### The average number of transitions to a particular state from only two particular states.

I know that in a Markov chain, $$\mathbf{N} = (\mathbf{I} - \mathbf{Q})^{-1}$$ gives a matrix to calculate the expected number of times before absorption that a particular [transient] state is visited,...
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### Probability Density Function Example Help

I am reading through the text, "Introduction to Probability Theory with Contemporary Applications" by Lester Helms. I am stuck on the attached example. I understand how the author obtained the joint ...
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### Find a 95% upper confidence bound for lognormal dispersion

Let $X_1,\ldots,X_n$ be a sample from a population $X$. Assume that $X$ has a $lognormal$ distribution $(2,\sigma^{2})$, with $\sigma^{2}$ an unknow parameter. Find, for the variance of the population,...
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### Combinatorics on the word Abracadabra

How many different 'words' can be created using all the characters of 'ABRACADABRA'? In how many of the 'words' that there are no identical characters one next to the other? So, For the first part, ...
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### Means and Covariances of powers of a normal distribution

Let $X$ be a normally distributed random variable, with mean $\mu$ and variance $\sigma^2$. Consider a random vector $$V = \left[ X^n, X^{n-1}, \dots, X^2, X, 1 \right]^T$$ What is the expected ...
Let $(X_n)$ be a sequence of positive random variables. Suppose that the limit of expectation of this sequence $\lim_{n\rightarrow\infty}\mathbb{E}[X_n]=0$. This imply that $(X_n)$ converges to zero ...