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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
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4
answers
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Intuitive explanation to Probability question [closed]
I have \$3. I flip a coin. If I get heads, I get \$1. If I get tails, I lose \$1. The game stops when I have \$0 or \$7. What is the probability I get \$7?
I solved this by creating a system of linea …
4
votes
2
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Probability Question
You have $N$ boxes and $M$ balls. The $M$ balls are randomly distributed into the $N$ boxes. What is the expected number of empty boxes?
I came up with this formula:
$\sum_{i=0}^{N}i\binom{N}{i}\lef …
3
votes
2
answers
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Expected value of a gamma-distributed random variable to the n-th power?
Is there a closed form for $E(Y^n)$, where $Y$ is a random variable with a gamma distribution with parameters $\alpha$, $\beta$?
2
votes
1
answer
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Statistical test comparing two relative frequencies
I'm working with four populations consisting of true/false events. They each have a different mean and variance. I have samples from each, with different sample sizes. Call the percentage of observed …
3
votes
3
answers
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Is the min function ever an unbiased estimator for the mean?
Given $n$ i.i.d. variables $X_1$ to $X_n$ with an unknown probability distribution, the sample average is an unbiased estimator for the mean of the distribution. Is there some non-trivial probability …