Question

Here is a uniform probability distribution.

Answer 1

a) $P(4\le X\le6)=\dfrac25$ 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).