00:01
Okay, we have here three coins being thrown and we'll let x equal number of heads that appear.
00:10
Now, begin with none.
00:13
No heads appearing means i get tail followed by tail, followed by tail if i throw it three coins.
00:22
And p of three tails will be one half cubed or one at an eight.
00:31
Is a one eighth chance of getting no heads.
00:37
Getting one head is going to be either head, tail, tail, tail, tail, or tail, tail, tail, tail.
00:49
Three ways to get exactly one head.
00:52
Each line is the same chance, one half cubed.
00:57
So we get here three out of eight.
01:01
Now to get two heads, it could be head, head, tail, head, tail, head, or tail, head, head.
01:11
Again, three ways to get exactly two heads, and each line is the same chance, one -eighth.
01:18
So again, three out of eight.
01:21
To get three heads would be just head, follow by head, follow by head, and that is a one -eighth chance.
01:35
If you add up the bottom line, you can see we get one, which you must do.
01:39
Okay, that's the table then.
01:41
Require for part a now part b what they want is the chance p is one or above so p of x more than or equal to one so it could be this this or this one two or three add them up and we get seven over eight so x one or above seven aides then i want to work out the mean the value of this or see then the mean you is the expected value of x e of x and define that is sigma x times p of x equals x so what we have here then is zero times one over eight plus one times three over eight plus two times three over eight plus two times three over eight plus 3 times 1 over 8.
02:58
So we get 0 plus 3 8s, plus 6 over 8, plus 3 over 8, and that will be 12 over 8, which is 3 over 2, or 1 .5.
03:19
The mean value is 1 .5.
03:23
Now to work out the variance, this is part d, so the variance of x is going to be sigma...