00:01
In this question, we are told that there were 93 major earthquakes over the last 100 years.
00:07
And then we're asked to use the plusan distribution to find some probabilities.
00:13
So if we denote a random variable x as the number of earthquakes in a given year, we can say that x follows a plesson distribution with a mean of 93 divided by 100 or 0 .93, major earthquakes per year.
00:47
The probability function for the poisson random variable is general given by this formula.
01:02
So for this particular distribution, the probability function is .93 to the exponent x times e to the minus .93 over x factorial.
01:23
For part a we want the probability that in a given year there are no earthquakes, no major earthquakes.
01:30
This is the probability that x is equal to zero.
01:32
And using the poisson probability function, this simplifies to e to the minus .93.
01:43
It comes out to a probability of approximately .3946...