# 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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### Normal distribution

can anyone help me calculate $E(Z^4)$, $E(Z^3)$ for $Z\sim N(0,1)$? I know that $Z^2\sim \chi^2(1)$ then $E(Z^2)=1$, $Var(Z^2)=2$. Thank you.
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### What is probability that a team reaches final if we know the probabilities of all opponents in the semi-final?

Our Discrete Math professor asked us a question as the Euros are going on. Given the following info, what is the probability that Portugal will make it to the final? Win Probabilities in quarter ...
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### Kolmogoroff 0-1 does this proof work?

I have thought at this proof of the Kolmogorov 0-1 Law varying a little the sketch found in Probability essentials (Jean Jacod, Philip Protter). My questions are Is it a valid proof? Is it a bad ...
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### given the following CDF, find the expected value

I got stuck at the middle of the question. would appreciate your help. first of all, given the CDF as follows, I had to find parameters $a$ and $b$ such that the CDF is a function of a continuous ...
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### Probability of Elements belonging together

Imagine a camera scene, where an algorithm labels the person which are inside from 1 to n. Now, imagine there is not just one perspective, but multiple. That means multiple cameras looking at the same ...
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### Determine probability based on observation

Suppose there is an urn with 100 balls, of two colors, say white and black. Let $p$ be the probability of drawing a white ball. You draw one ball, replacing after the draw. After 100 draws, each with ...
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### Conditional expectation of the sum of three dice rolls given the sum of their maximum and product

Consider the random experiment in which three fair dice are rolled simultaneously (and independently). Let $X$ be the random variable defined as the sum of the values of these three dice. Let $Y_1$ ...
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### Weak Law of Large Numbers

The Weak Law of Large Numbers is often stated with the iid assumption for the underlying RV's. However, I have seen the independence assumption being diluted to the "uncorrelatedness" assumption (e.g.,...
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### Expected number of balls from throwing between boxes

I have 6 boxes: $A,B,A',B',C \text{ and } D$. The box $A$ has $n_1$ red balls that are numbered from $1, \cdots, n_1$. The box $B$ has $n_2$ green balls that are numbered from $1, \cdots, n_2$. Make a ...
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### Conditional Probability for a Poisson Distribution: X = 1 | X $\geq$ 1

Suppose X has a Poisson distribution with a standard deviation of 4. What is the conditional probability that X is exactly 1 given that X $\geq$ 1? I know that for this problem $\lambda$ is 16 ...
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### Probability of one Poisson variable being greater than another

Given two Poisson distributions with different λ values, if each were to produce a single random variable, is there closed-form expression for calculating the probability of one random variable being ...
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### Compute conditional probability

If a conditional probability table is given for $P(S_t|M,E)$. How to compute the value for $P(S_t = x | M,E)$ ? where $E$ is binary (0 or 1) and $M$ is ternary ?
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Let $X(t)$ be a Brownian motion in $\mathbb{R}^n$, stopped at some fixed time $T$. Is there a notion of Green's function for such a Brownian motion? I am guessing that there is, and $G(x, y) : = \... 4answers 94 views ### why is Probability (at least one solved$ =$P(A\cup B)$

I have a question in which it is stated that the probability of a student solving a problem A is $\frac{2}{3}$. And the probability of solving another problem B is $\frac{3}{5}$. So what is the ...
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### How much larger is the Likelihood Function Under True Model?

Let $X$ be a random variable with probability distribution functions given by $f$, and let $g \neq f$ (on a set of positive measure) be some other distribution. $D=\{x_1, \ldots, x_n\}$ is a set of $n$...
I've been struggling with a problem a CS student friend of mine gave me a few hours ago. Given that $P$ is an array of integers and $N$ is its size, how many minutes is the following algorithm ...