 # Computing the integral of g on 1 1 we get z 1 1 g x

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Computing the integral ofgon (-1,1) we getZ1-1g(x)dx=Zb-bcos(x)dx= 2 sin(b).There is one solution for 2 sin(b) = 1 forb2[0,/2], it isb= arcsin(1/2) =/6. Forthis choose ofbthe functiongis a pdf.
3.9 Suppose that the random variableXhas cumulative distribution function given byF(x) =8>>>>>><>>>>>>:0,ifx <1,1/3,if1x <32,1/2,if32x <53,3/4,if53x <95,1,ifx95.(a) Find the range ofX.(b) Show thatXis discrete, and find its probability mass function.
Solution:
3.13 Choose a point uniformly at random in a unit square (square of side length 1). LetXbe the distance from the point chosen to the nearest edge of the square.(a) Find the cumulative distribution function ofX.(b) Find the probability density function ofX.

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Term
Fall
Professor
BALAZS
Tags
Math, Probability theory, Cumulative distribution function, CDF
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