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How to find the expected value of the first order statistic

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#probability #statistics #independence #expected-value #order-statistics
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What is the moment generating function of the Laplace distribution?

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#probability #probability-distributions #expected-value #moment-generating-functions
137
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If $X_1,X_2 \sim N(\mu,\sigma^2)$ , then find $E[(X_1+X_2)^2|X_1=X_2]$

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#probability #probability-theory #probability-distributions #normal-distribution #expected-value
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Nonnegative continuous functions on $[0,1]$ attaining maximum value in $\{0,1\}$

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#real-analysis #ordinary-differential-equations #optimization #expected-value #non-convex-optimization
99
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Naive question about expectation: how do we prove that $\textbf{E}(X) = \int_{0}^{\infty}\textbf{P}(X > x)\mathrm{d}x$?

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#integration #probability-theory #expected-value
77
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If $X\sim\text{Exp}(\lambda)$, then $\textbf{E}(X^{n}) = \displaystyle n\textbf{E}(X^{n-1})/\lambda$

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#probability-theory #expected-value #exponential-distribution
32
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Simplifying large, expanded sums

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#summation #expected-value #symmetric-functions
650
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Expected distance squared of random walk on an infinite hexagonal grid

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#probability #random-walk #expected-value
61
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Expected value of different types of sample means

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#probability #statistics #summation #normal-distribution #expected-value
60
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Finding Expectation using CDF

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#statistics #expected-value
54
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finding the pdf and expected value of first order statistic

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#probability #expected-value #order-statistics
41
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Expected value of random variables' sample means

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#statistics #normal-distribution #variance #expected-value
24
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How to prove tail sum formula of XY, given that X and Y are jointly distributed and non-negative?

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#probability #expected-value
104
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Find the expected value of the sum of numbers without knowing them

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#probability #expected-value
88
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gamblers fortune expectation[ith game winnings] = 0. Why?

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#martingales #expected-value

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