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