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If $X, Y, Z$ are positive i.i.d. r.v.s, why is $E(\frac X{X+Y+Z})=E(\frac Y{X+Y+Z})=E(\frac Z{X+Y+Z})$?

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#probability #random-variables #expectation
156
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Martingale and Super-Martingale

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#probability-theory #stochastic-processes #expectation #martingales #polya-urn-model
57
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How to compute basic statistics of the time series $Y_j = A \sin(\theta \times j) + Z_j$

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#statistics #stochastic-processes #expectation #variance #time-series
61
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Poisson Random Variable As Parameter Approaches $\infty$

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#probability #random-variables #expectation #infinity #poisson-distribution
6.1k
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Probability of Coin toss With Poisson Distribution

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#probability #probability-distributions #random-variables #expectation #poisson-process
446
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Median of Random Variable

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#probability #probability-distributions #random-variables #expectation #median
630
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Derive PDE from $n^{\text{th}}$ moment of stopping time of SDE

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#partial-differential-equations #stochastic-processes #expectation #stochastic-calculus #stopping-times
103
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Dependence of expectation operator on order properties of sample space

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#probability #probability-theory #measure-theory #expectation
81
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Random Walks with independent symmetric relations

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#probability #random-variables #expectation #random-walk
271
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If we have infinite variance, can the expectation 'mean' anything?

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#probability #expectation #variance
138
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Expectation normal distribution

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#exponential-function #normal-distribution #expectation
311
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Finding mean first passage time for reflecting Brownian motion

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#ordinary-differential-equations #partial-differential-equations #expectation #stochastic-calculus #stochastic-differential-equations
102
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Where is the mistake in the argument? (And two conjectures)

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#probability #proof-verification #expectation #conjectures #divisor-sum
35
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How do I find the expected value of trials to achieve an amount of successes in a row?

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#probability #expectation
264
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Is the series $X_j = Z_0 \cos(c j)$ stationary?

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#expectation #covariance #variance #time-series #stationary-processes

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