An ensemble member of a stationary random process X(t) is sampled at N times t₁, i = 1, 2, ..., N. By treating the samples as random variables X; = X(t), an estimate or measurement й of the mean value X process is sometimes formed by averaging the samples: = E[X(t)] of the For the random process and samples defined in Problem 8 let an estimate of the variance of the process be defined by =- 1 N N Σ (Χ, - 82 Show that the mean value of this estimate is N-1 E[0] στ N

An ensemble member of a stationary random process X(t) is sampled at N times t₁, i = 1, 2, ..., N. By treating the samples as random variables X; = X(t), an estimate or measurement й of the mean value X process is sometimes formed by averaging the samples: = E[X(t)] of the For the random process and samples defined in Problem 8 let an estimate of the variance of the process be defined by =- 1 N N Σ (Χ, - 82 Show that the mean value of this estimate is N-1 E[0] στ N

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 10E

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