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Problem 6. Consider a random variable X whose cumulative distribution function (cdf) is given by 0 0.1 0.4 0.5 0.5 + q if -2 f 0 r< 2.2 if 2.2<a<3 If 3 < x < 4 We are also told that P(X > 3) = 0.1. (a) What is q? (b) Compute P(X2 -2> 2) (c) What is p(0)? What is p(1)? What is p(P(X S0)? (Here, p(.) denotes the probability mass function (pmf) for X) (d) Sketch a plot of the function p(x). (Make sure to label the coordinates on the axes!) (e) What is P(2X -322 X 2 2.1)? (f) Compute E(X) (g) Compute E(X2) (h) Compute var(X)

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Answer #1

0.5 , if 2.22 <3 1 if 4, re, 1-10-5+4) =0-1

ply) 0 .9 o.6 明 o -2 -2-1 į 2.2.2 3 4 22 -F2) 0,5 下. 0.2 + 0.22+ 1.2+0.4 1.62 6.08t,

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