Choose a point uniformly at random from a rectangle with height 1 and width 3. (This means that the probability of the point landing in any region is the area of the region divided by the area of the entire rectangle.) LetXbe the distance from the point to the nearest edge of the rectangle.

1. Find a formula forF(x), the cumulative distribution function ofX, when0x1/2, Note that F(x)=0whenx<0 andf(x)=1whenx>1/2, (Why?) This is why the question only asks for the cdf forxbetween 0 and 1/2. F(x) =
2. Find a formula for the probability density functionf(x)ofXfor0x1/2. f(x)=