Let Y1 Y2 and Y3 be three random points chosen independently

Let Y1, Y2 and Y3 be three random points chosen independently and uniformly from (0, 1), and let X be the rightmost (largest) point. Find the cumulative distribution function., density function, and expectation of X.

Solution

Y1 Y2 Y3 have uniform distribution from (0,1)

pdf = 1, 0

X is the maximum of y1,y2,y3

x can take values between 0 and 1.

CDF X = x, 0

PDF of x =1, 0

E(X) = 1