[機統] 關於機率論的連續隨機變數問題!
(a) Suppose that U ~ uniform(0; 1) and that F is a strictly increasing
CDF corresponding to a continuous random variable.
What is the distribution of X = F^-1(U)?
(b) For a parameter α > = -1, consider the density function
f(x) =(1 + αx)/2; -1 < = x < = 1:
How could random variables with the density f be generated from
a uniform random number generator?
(c) The Weibull distribution with parameters α;β> 0 has CDF
F(x) = 1 - e^-(x/α)^β; x > = 0:
How could Weibull random variables be generated from a uniform random number
generator?
(d) Suppose you have access to infinitely many independent Bernoulli(p)
random variables.
How can you generate a Bernoulli(0:5) random variable?
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