1. In a lot of n components, 30% are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective,….

## estimate the time since the most recent cooling of a mineral by counting the number of uranium fission tracks on the surface of the mineral

1. Let X ∼ Poisson(4).

a. Find P(X = 1)

b. P(X = 0)

c. P(X <>

d. P(X > 1)

e. µx

f. µx

2. The number of pits in a corroded steel coupon follows a Poisson distribution with a mean of 6 pits per cm2 . Let X represent the number of pits in a 1 cm2 area.

a. Find P(X = 8

b. ) P(X = 2)

c. P(X <>

d.

e. P(X> 1) µx

f. µx

3. The number of large packages delivered by a courier service follows a Poisson distribution with a rate of 5per day. Let X be the number of large packages delivered on a given day. Find

a. P(X = 6)

b. P(X ≤ 2)

c. P(5 <><>

d. µX

e. σX

4. Geologists estimate the time since the most recent cooling of a mineral by counting the number of uranium fission tracks on the surface of the mineral. A certain mineral specimen is of such an age that there should be an average of 6 tracks per cm2 of surface area. Assume the number of tracks in an area follows a Poisson distribution. Let X represent the number of tracks counted in 1 cm2 of surface area. Find

a. P(X = 7)

b. P(X ≥ 3)

c. P(2 <>< 7)=””>

d. µX

e. σX