00:01
The probability mass function for the poison distribution is given by p of x equals k equals lambda to the k times e to the negative lambda over k factorial.
00:14
And so for a mean of four, then a lambda is equal to four.
00:21
And then for a we want the probability that x is zero.
00:26
And so that would be four to the zero times e to the negative fourth over zero which calculates, let's say, what to round two.
00:42
I'm going to go four decimal places.
00:46
0183.
00:52
The probability that x is less than equal to 2 would be the probability that x is equal to 0 plus the probability of that x is equal to 1 plus the probability that x is equal to 2, which would be 4 to the 0, e to the negative 4th, 0 factorial plus 4 to the 1st, e to the negative 4th over 1 factorial, plus 4 squared e to the negative 4th over 2 factorial, which calculates to 0 .2381 for c, the probability that x equals 4 would be equal to 4 to the 4th, e to the negative 4th over 4 factorial and that calculates 0 .1954 and d probably that x is equal to 8 would be 4 to the 8 times e to the negative 4th over 8 factorial or 0298 and then repeat this for a mean of 0 .094.
02:25
So for a, the probability that hits 0 would be 0 .4 to the 0 times the e to the negative 0 over 0 factorial, which calculates to 0 .6703, less than are equal to 2...