5. A continuous random variable X follows a uniform distribution over the interval [0, 8]. (a)...

Question

Question

Answer 1

Answer #1

a) X ~ U (0 , 8)

P(X < x) = (x - 0) / (8 - 0)

P(X > x) = (8 - x) / (8 - 0)

P(X > 3) = (8 - 3) / (8 - 0) = 0.625

b) To be a valid probability distribution, total area must be equal to 1.

Area = 1/2 * 8 * h

or, 1 = 4 * h

or, h = 0.25

f(x) л а 0 - 0 3 8

We need to find a.

According to similarity of triangle, a/h = (8-3)/8

or, a/0.25 = 5/8

or, a = 0.15625

P(X > 3) = 1/2 * 0.15625 * (8 - 3)

= 0.390625

Answer 2

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