Question

Here is a uniform probability distribution.

A) What is P(4 ≤ X ≤ 6)? Explain.

B) If P(X ≤ a) = 0.2, what is a? Explain.

Answer 1

a)
`P(4\le X\le6)=\frac25` because it is equal to the area of the shaded region between X=4 and X=6, and the probability that X falls within some interval is given by the area under the PDF.

b)
`a=3` because the shaded region is a rectangle of height 1/5 (by virtue of X following a uniform distribution over the interval [2, 7], which has length 5).