00:01
So x is a randomly selective positive integer from this set, 5, 6, 7 and 8.
00:07
And we want to compare the expectation of x tripled, so that's 3, mu of x, mu being the mean, also the expected value, they're synonyms, to the expectation of triple x.
00:25
Will they be equal? will one be larger, y? so to find the expectation or mean of a variable, you take each possible outcome, you multiply it by its probability, and you add these up.
00:37
So this would be mu of x.
00:40
Okay, let's have a look at mu of 3x.
00:43
So i'm just going to tick the x and everything is just tripled.
00:46
So that would be the sum of 3x times p of x.
00:56
So 3 mu x is 3 times this.
00:59
Mue of 3x has the 3 in here, but the outcomes are going to be the same.
01:06
So because the probabilities sum to 1 for a valid probability distribution, what you get is each of these is a fragment of 1, and you're adding them all up...