Compute the following probability:?

Question

f(x) = (3/8)x^2 for 0<x<2

Compute:

Pr(0 < X < 1/2 ∪ 1 < X < 2)

Answer 1

Hint: For continuous data, to find the probability that 0 &lt; X &lt; 1/2,

you integrate over the bounds given, such that:

1/2

∫ (3/8)x² dx

0

= [3/8 * 1/3 x³] from 0 to 1/2

= 3/24x³

= [3/24 *(1/2³) - 0]

= 3/192  &lt;~~ This is P(0&lt; X &lt;1/2)

Now, find P(1&lt; X &lt; 2) and think about the definition of ∪

I hope this helps a bit.