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The density of a random variable X is given by x 0 < x < 1 f(x) = 2 - x 1 < x <
The density of a random variable X is given by
x 0 < x < 1
f(x) = 2 - x 1 < x < 2
0 Otherwise
A) Find E l X l
B) Find the CDF of X. Write the following Probability in terms of the CDF of X and then compute it; P(X < 3/2 l X > 1/2)
C) Let X1, X2,......., X100 be i.i.d random variables with the same distributions as X. What is the distribution of the number of Xi's such that 1/2 < Xi < 3/2
Write the expression for the chance that exactly 75 of the Xi's are below 0.5.
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