You have been given the data (5000 samples) of a random variable Z. You know that Z= x+10y where X is a uniform random variable between -3 and 3. You also know that y= ∑_(i-1)^k▒w_i where k ∈ {2,3,4}, w_i’s are independent and identically distributed and belong to one of the following
Exponential distribution characterized by its mean 1⁄λ
Rayleigh distribution characterized by σ
Half normal distribution characterized by σ
Come up with a mechanism to find k and the distribution of W_ialong wit the characterizing parameter rounded to the nearest integer. Justify your mechanism analytically.
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B2
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