Question

Suppose f(x) = 1/4 over the range a ≤ x ≤ b, and suppose P(X > 4) = 1/2.

What are the values for a and b?
-0 and 4
-2 and 6
-Can be any range of x values whose length (b − a) equals 4.
-Cannot answer with the information given.

Answer 1

a=2

b=6

Explanation:

Assuming a uniform distribution and that a ≤ x ≤ b, if f(x) = 1/4, then:

`f(x) =(1)/(4)=(1)/(b-a)\\b-a = 4`

If P(X > 4) = 1/2, then:

`(1)/(2) = 1-((x-a)/(b-a))=1-((4-a)/(4))\\a-4+4 =(1)/(2)*4\\ a=2\\b=4+a\\b=6`

The values for a and b are, respectively, 2 and 6.