00:01
Hello everyone, in this question we need to consider the sequence of bernoulli trials.
00:07
And here we are given that x that is equal to the number of trials needed until the first success.
00:15
And then x has a geometric distribution with the parameter p.
00:22
We need to find the variance of x.
00:26
So first of all, we can write p of x that is equal to k, that is equals to 1 minus p, raise to k minus 1 multiplied by p.
00:39
So now we need to variac of x and let y that is equals to outcome of the first cross.
00:51
So variac of x that is equal to variac of x.
00:59
Of x divided by y plus e variance of x divided by y.
01:08
Now let y is equal to 0 if failure.
01:15
That implies that x that is equal to 1 plus x star where x star x star that merely equals to the x.
01:28
Now, y that is equals to 1 if success.
01:36
So that implies that x is equal to 1 and it is done.
01:40
So that implies that e of x divide by y that is equals to 1 if y is equal to 1 and 1 plus e of x if y is equal to 0...