Probability and Random Processes. A continuous random variable is said to have a Rayleigh distribution with parameter

Probability and Random Processes.

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A continuous random variable is said to have a Rayleigh distribution with parameter o if its PDF is given by for a >= 0 fx(x): o2 for a <0 (a) If X~ Rayleigh(o), find E[X]. (b) If X ~ Rayleigh(o), find the CDF of X. (c) If X~ Exponential (1) and Y = V20²X, show that Y Rayleigh(0). ~ A continuous random variable is said to have a Rayleigh distribution with parameter o if its PDF is given by for a >= 0 fx(x): o2 for a <0 (a) If X~ Rayleigh(o), find E[X]. (b) If X ~ Rayleigh(o), find the CDF of X. (c) If X~ Exponential (1) and Y = V20²X, show that Y Rayleigh(0). ~