You are using the following procedure to simulate a random variable
Y
: Generate 3 uniform random variables
U_(1),U_(2),U_(3)∼Unlform(0,1)
. For
i=1,2,3
, set
x_(i)=-2ln(1-U_(i))
. Set
Y=min(x_(1),x_(2),x_(3))
. Calculate the variance of the resulting random variable
Y
.

Question

You are using the following procedure to simulate a random variable

Y

: Generate 3 uniform random variables

U_(1),U_(2),U_(3)∼Unlform(0,1)

. For

i=1,2,3

, set

x_(i)=-2ln(1-U_(i))

. Set

Y=min(x_(1),x_(2),x_(3))

. Calculate the variance of the resulting random variable

Y

.

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