Question

If a day is equivalent to 10 million years (i.e. 10^7 years), all of Earth's geological history corresponds to about 450 "days". The history of life on earth corresponds to about one "year".  If a catastrophic meteorite impacts occur about every 100 million years, or 10 "days" in our time scale, we can model the time ? between catastrophic meteor impacts with an exponential random variable, with mean 10.

a) Compute the probability ?(?≤6.5)

b) Compute the conditional probability ?(?≥7.5|?≥6.5)

c) Assuming a Poisson point process model with an intensity of ?=1/10 major meteors per "day", what's the probability of two major meteor impacts occurring on the same "day".

Answer 1

a)

Here

So,

Required probability =

b)

Required probability =

c)

Let X denote the number of major metros per day. Then

Required probability =