Consider a probability density function (PDF), where f(T-t) is a general function, g(T) and h(t) are time-dependent functions. (a) Calculate the first moment of the PDF. (b) Calculate the second moment of the PDF. (c) Calculate the variance.

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Consider a probability density function (PDF), where f(T-t) is a general function, g(T) and h(t) are time-dependent functions. (a) Calculate the first moment of the PDF. (b) Calculate the second moment of the PDF. (c) Calculate the variance.

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1
(Xo – X7)²
P(Xr,T;Xo,0) =
exp
(2ng(T)² S,'[F(T – t)h(t)]² dt /
2g(T)² S'If(T – t)h(t)]² dt,
Transcribed Image Text:/2 1 (Xo – X7)² P(Xr,T;Xo,0) = exp (2ng(T)² S,'[F(T – t)h(t)]² dt / 2g(T)² S'If(T – t)h(t)]² dt,
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