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20092ee132B_1_hw2sol

# 20092ee132B_1_hw2sol - UCLA Electrical Engineering...

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Unformatted text preview: UCLA Electrical Engineering Department EE132B HW Set Solution #2 Professor Izhak Rubin Solution to Problem 1 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 2 2 2 2 2 2 2 4 2 2 2 2 2 2 2 2 2 1 2 2 1 2 2 2 1 2 2 2 1 1 2 2 2 2 1 2 2 1 2 1 2 1 2 1 2 sX X x sx x s x x s s s x s s s s s s E e e e dx e dx e dx e e dx e μ σ μ σ μ σ μ σ μσ σ σ μ σ μ σ σ μ σ πσ πσ πσ πσ--- ∞--∞ --- + ∞ -∞ --- +- ∞ -∞----- ∞-∞-- Φ = = = = = = ∫ ∫ ∫ ∫ ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 2 2 2 2 2 2 2 Using the moment generating function, the mean and the variance of is calculated as follows. lim 1 lim 2 2 2 lim 1 lim 2 2 2 X s X s X s X X s X d E X s ds s s d E X s ds s s s Va μ σ μ σ μ σ σ μ → → → → = - Φ = --- Φ = = Φ = Φ +- Φ = + ∴ ( 29 ( 29 ( 29 2 2 2 r X E X E X σ =- = Solution to Problem 2 ( 29...
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20092ee132B_1_hw2sol - UCLA Electrical Engineering...

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