00:01
In this problem, the random variable x follows poison distribution with probability density function, e power minus lambda, lambda, power x divided by x factorial, where x takes the value 0, 1, 2, 3, 4, etc.
00:15
Okay, and now we are taking x represents the number of accidents happened weekly, that is number of weekly accidents and lambda equal to 7 .3.
00:26
Now we have to find e of x.
00:29
So, e of x is summation x equal to 0 to infinity, e power minus lambda, that x times, e power minus lambda, lambda power x divided by x factorial, which is equal to lambda we can take outside, summation x equal to 0 to infinity, e power minus lambda, and this one can be written as lambda power x minus 1 divided by, and these two terms we can cancel out and we will get it as x minus 1 factorial.
00:56
Because x factorial can be written as x minus 1 factorial multiplied by x.
01:01
Okay, which is equal to lambda times e power minus lambda, summation x equal to 1 to infinity, lambda power x minus 1 divided by x minus 1 factorial, which is equal to lambda times e power minus lambda multiplied by e power lambda, which is equal to lambda...