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

Answer:

a=2

b=6

Step-by-step explanation:

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

$f(x) =\frac{1}{4}=\frac{1}{b-a}\\b-a = 4$

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

$\frac{1}{2} = 1-(\frac{x-a}{b-a})=1-(\frac{4-a}{4})\\a-4+4 =\frac{1}{2}*4\\ a=2\\b=4+a\\b=6$

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