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Starting from a uniform distribution between

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1. Starting from a uniform distribution between (0,1). 

i. Generate a sequence of Rayleigh distributed random variable. (parameters: a=0, b=1).

ii. Generate a sequence of exponentially distributed random variable. (parameters: a=0, b=1)

iii. Generate a sequence of Gaussian random variable. (parameters: a=0, σ2/x = 4)

2. Check the validity of the random variables generated in parts 1 by

i. normalized histogram and comparing it with the theoretical pdf.

ii. estimating the mean and variance and comparing it with the theoretical values.

3. Verify the central limit theorem (CLT):

i. For a set of sequences of independent identically distributed (i.i.d.) random variables. (use the Rayleigh r.v. generated in step 1)

ii. For a set containing sequences of a mix of independent random variables.

Reference no: EM13867681

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