00:01
So we're told that the number of accidents is described by a poisson distribution.
00:07
So i'm going to let x equal number of accidents.
00:14
And our rate of occurrence, lambda, is given as 1 .5 for every three months.
00:29
So the probability that x is any number of accidents will be given by our poisson formula, e to the power of negative lambda times lambda to the power of x over x factorial.
00:48
So the probability that in three months there are zero accidents will be given by e to the power of negative 1 .5 times 1 .5 to the zero power over 0 factorial, which is 0 .223.
01:06
The probability that there are less than four accidents in that time frame will be given by the probability x equals 0 plus probability x equals 1 plus probability x equals 2 plus probability x equals 3.
01:28
So filling out our poisson distribution for all of those, e to the negative 1 .5 times 1 .5 to the 0 over 0 factorial.
01:43
Plus e to the negative 1 .5, 1 .5 to the first power, over 1 factorial, e to the negative 1 .5 times 1 .5 to the second power over 2 factorial, plus e to the negative 1 .5 times 1 .5 to the third power over 3 factorial.
02:13
So solving those will get 0 .22 .2.
02:18
Plus 0 .3347 plus 0 .251 .02 plus 0 .125 .5.
02:30
For a total probability that x is less than 4 of 0 .934...