What is the probability that a uniform random variable with limits of a = 2 and b =
10 is less than or equal to 5?
A.0.375
B.0.500
C.0.625
Correct Answer : A
A is correct because "the middle line of the expression for the cdf [of the continuous
uniform distribution] captures this relationship:
0 for x < a
F(x) = x-a / b-a for a ≤ x ≤ b.
1 for x > b"
For our problem, F(x) = 0 for x < 2, F(x) = (x-2)/8 for 2 ≤ x ≤ 10, and F(x) = 1 for x > 10.
Hence, F(5) = (5- 2)/8 = 0.375.
