Question

suppose X and Y are independent random variables that follow the uniform distribution on the interval [0,1]. Let Z=min{X,Y}. P(Z<0.5)=?

Answer 1

Due to X, Y are independent, one can write P(Z > 0.5) = P(X, Y >0.5) = P(X > 0.5)P(Y > 0.5) = 0.5 · 0.5 = 0.25