Prove that the mean the expectation and the variance

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Reference no: EM132505235

Probability Background

Prove that the mean E(x), the expectation E(x²) and the variance σ²_x by using

a- PDF p(x), where

E(x) = _-∞∫^∞ x p(x) dx

E(x²) = _-∞∫^∞ x² p(x) dx
-∞
σ²_x = E(x²) - (E(x))² .

b- Characteristics function, where

ψ(jv) = _-∞∫^∞ e^jvx p(x) dx

E(x) = -j dψ(jv)/dv|_v=0

E(x)² = (-j)²d²ψ(jv)/dv²|_v=0

σ²_x = E(x²) - (E(x))²

for the following distributions:

1- Uniform Distribution

2- Chi-Square Distribution

3- Rayleigh Distribution

4- Rician distribution

Attachment:- Probability Background.rar

Reference no: EM132505235

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