The probability density function of the contamination partic

The probability density function of the contamination particle size (in micrometers) can be modeled as f(x) = 2x^3 for 1

Solution

14)

mean = x* p(X)

= 0 * 0.1+ 01 * 0.15 + 2 * 0.25 + 3 * 0.25 + 4 * 0.15 + 5 * 0.1

= 2.5

15

variance = E(Xˆ2) - meanˆ2

=0 * 0.1 + 1ˆ2 * 0.15 + 2ˆ2 * 0.25 + 3ˆ2 * 0.25 + 4ˆ2 * 0.15 + 5ˆ2 * 0.1 - 2.5ˆ2

= 2.05

16)

P(A or B)

= 4/5 + 5/6 - 3/4

= 53/60

17)

P(B) = 2/6

P(A) = 3/6

P(B and A) = 1/6

P(B/A) = P(B and A)/P(A)

= 1/6/3/6

= 1/3