# 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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### Checking if a coin is fair [on hold]

I want to check if a coin is fair (lands 50% of the times on each side). I flip that coin multiple times and count the number of times it fell on heads and the number of times it fell on tails and ...
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### Flipping coins- percentages of heads vs tails [on hold]

If I flip a coin multiple times and count the number of time it fell on heads and the number of times it fell on tails and keep a track of them. In how many flips on average will the delta between ...
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### Existence of Joint Distribution from Overlapping Marginal Distribution

Suppose $x_i\in \mathbb{R}^{n_i}$ for $i=0,1,...,k$. For each $i=1,...,k$, suppose $F_i$ is a probability measure of $(x_0,x_i)$ on $\mathbb{R}^{n_0 + n_i}$. Assume all $F_i$ have the same marginal ...
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### why probability is multiplied in finding out dependent probabilities?

Why is probability multiplied in case of dependent events? When we want to find out say, We take out a card from a deck of 52 cards and take another without replacing, We get the probability of ...
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### sampling requirements in probabilistic polynomial identity testing

In the Schwartz–Zippel algorithm for bounded error probabilistic polynomial identity testing, the main theorem is the following: For a non-zero multivariate polynomial $p(x_1,...,x_n)$ of total ...
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### Card Probability Without Replacement

So there are 15 cards total, 5 red, 7 orange, and 3 yellow. At random you pick 3 (no replacement). What's the probability of picking: 1) Exactly 2 Red? 2) Not more than one yellow? 3) One of each? ...
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### Average Goals Per Game

Okay I am trying to work something out. If for example Team A scored an average of 2.84 goals per game over a period of 95 matches. What is the probability that there next match will be 3 goals or ...
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### Suggestions for Constructing a Random Variables from Correlated Observations

Let $\mathcal{X} \neq \phi$ be a finite set. Let $P_{XY_1Y_2}$ be a fixed joint distribution over $\mathcal{X}\times\mathcal{X}\times\mathcal{X}\$ and that a random sample $(X,Y_1,Y_2 )$ is drawn ...
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### Deriving global probabilities from local dynamics

I am interested in growth dynamics and, in particular, how to derive difference/differential/stochastic equations from local behavior of a system. For concreteness, let's imagine a simple predator/...
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### Finding probability with the help of combinations

$N$ tutors are to be assigned to $s$ students with any student having at most one tutor and similarly any tutor having at most one student. If any tutor is assigned randomly then how can we find the ...
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### Value of c so that $c(2-|x|-|y|)$ is a probability distribution function(see picture)

Hint: Use the formula of volume of pyaramid. My approach: I know that the integral of a pdf from $-\infty to +\infty$ gives you $1$. I tried taking the double integral, but got stuck in as how to ...
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### Expected length of a random walk

Let $G = (V,E)$ be a connected graph. Now consider a random walk on $G$, where we pick a random vertex $v_0$ sampled uniformly at random from $V$. Let $v_i \in V$ denote the vertex in the current ...
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### Finding Future probability of results within a group of numbers

I apologize in advance if this question, or one similar, has been asked - I couldn't find anything via a quick search. How do I go about finding the probability of any particular number from within ...
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### Scale invariance of uniform distribution over $\mathbb R^2$?

If we make a uniform distribution of points over $\mathbb R^2$ with 1 point on average per unit square. And we zoom far out and make a density plot (give a color to each cell according to how many ...
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### Intuition of the expectation.

Let $(\Omega ,\mathcal F,\mathbb P)$ a probability space. What is the intuition behind the definition $$\mathbb E[X]=\int_\Omega X(\omega) \, \mathrm d \mathbb P(\omega )\text{ ?}$$ I don't see in ...
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### If you roll two six-sided dice, what is the probability that the dice add to 10 or higher?

When answering these sort of questions people mostly resort to diagrams and I'm wondering if there is a way to calculate the probability without going through each outcome, just solely on the given ...
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### Number of ways of writing an integer as a sum of other integers

Fix a non-negative integer $m$. For any integer $A \geq 1$, use $P_m(A)$ to denote the number of ways of rewriting $A = A_1 + A_2 + \ldots A_k$, with $1 \leq A_i \leq m$, for any $k \geq 1$. I ...
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### Integral that makes square root of $\frac{\pi}{2}$ [duplicate]

My question is regarding a integral that´s giving me a huge headache. I want to show $$\int_{0}^{\infty}y^2e^{-\frac{y^2}{2}}dy=\sqrt{\frac{\pi}{2}}$$ I'm studying for an exam. I'm suppose to find ...
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### Binomial distribution: dice [on hold]

A fair die is rolled five times. Find the probability of obtaining: a) all results greater than 3 b) a 5 on the first roll only c) a 5 on the second and third roll only
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### Probability that the second throw of a fair die exceeds the first

A player throws an ordinary die and records the score $A$. The player then throws the die again and again records the score, $B$. if $B>A$ then we set a score for this player. What is the ...
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### Difference between a mixture of distributions and a convolution. Intuition

From what I could gather Mixture: if $X_i\sim^{iid} f_i$, then W is a mixture with $f_W =\sum \frac{f_i}{n}$. This definition could also be for the CDF instead of the density. Convolution: To make ...
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### Help needed related to derivation

I want to find the following probability $$P(z_i\leq min(1,x^{-m})<z_{i+1}, x<x_1|z_i \leq 1, z_{i+1}>1)$$ where $m$ is some value greater than $2$, $z_i$'s are some constants and pdf of $x$ ...
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### Probability of being in a circle, given normal

Let's assume a bivariate normal distribution with center $\mu$ and covariance matrix $\Sigma$. Let a circle $C$ be given as $C=\{x\in\mathbb{R}^2:||x-\mu||\leq R\}$. I would like to calculate the ...
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### Probability - Poisson Arrival Process

Car arrive at a toll booth according to the Poisson process at a rate of 3 arrivals per minute. a) What is the probability that the third car arrives within 3 minutes of the first car? b) Of the ...
### For $X,Y$ random variables, $h$ a function, show that $E (Xh(Y)|Y)=h (Y)E (X|Y)$ almost surely
Question in the title: For $X,Y$ random variables, $h$ a function, show that $E (Xh(Y)|Y)=h (Y)E (X|Y)$ almost surely My main problem is that I don't even understand what $E (Xh(Y)|Y)$ means.....