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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determine the distribution of the random variable $Y=\Sigma_{k=1}^{\infty}kX_k$

Fix $p \in (0,1)$ and consider independent Poisson random variables $X_k$, $k \geq 1$ with $\mathbb E[X_k]=\frac{p^k}{k}$. Verify that the sum $\Sigma_{k=1}^{\infty}kX_k$ converges with probability ...
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probability question with marbles

I have $13$ different color marbles. One color is $5$ times likely to be chosen and another color is half as likely to be chosen. What is the probability that, $1$. you choose the marble that is 5 ...
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Coin toss related problem

What is the minimum number of times a fair coin needs to be tossed so that the probability of getting at least two heads is at least 0.96? Is there any shortcut way to calculate this?
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What does it mean if $cov(f(x1), f(x2))$ is positive in the context of LHS sampling?

If cov(f(x1),f(x2)) is positive, does that mean f is close to symmetric along x1 and x2? I am struggling to put this into understandable terms. Edit: The context is equation 6 in this paper: http://...
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CGF determines the distribution

It is well known, that if the domain of the mgf of a random variable $X$ contains an interval around zero, then the distribution is completely determined by its moments. However consider a Levy-...
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Event ($E_n$, i.o.): an exercise for understanding the definition

This is an exercise from David Williams' "Probability with Martingales" on page 28. I am studying on my own and I would appreciate some feedback on my proof. For an event $E$ define an indicator ...
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estimation for analytic stochastic processes

this is for experts in probability and stats. There is a theorem, I have seen once: Given a stationary analytic random process, one can show that from the values of a sample path in a finite interval ...
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