00:01
A roulette wheel has 38 slots.
00:03
36 are numbers 1 to 36, and then there's 0 and 0, 0.
00:09
Now, we're having a bet where the bettor pays $1 to play.
00:15
If a ball lands in an even number, he gets the dollar back, plus an additional dollar.
00:21
And if it doesn't land on an even slot, he just loses his dollar.
00:25
So we've got x, the gain for the bettor, and we're going to construct this probability distribution.
00:32
So what are the possible outcomes for the bettor here? they could win, in which case their net gain is $1.
00:42
They get the dollar back, they pay to play, plus this extra one, so a profit of 1.
00:47
Or they could lose, in which case they've lost a dollar.
00:51
What are the probabilities involved here? so there are 38 slots.
00:57
If we look at the numbered ones, half of those are even.
01:00
If we look at 0, 0 and 0, one of them is even, one of them is not.
01:05
So overall, out of the 36 slots, half of them are even.
01:12
So we have 0 .5 as the probability of winning, and 0 .5 as the probability of losing.
01:21
So if we look at 1 to 36, 18 of those are even, 18 are odd.
01:29
So there's 19 even and 19 odd slots on this board.
01:34
So here's our distribution.
01:35
We want to find the expected value, and the standard deviation as well.
01:40
To get the expected value of a variable, you take each possible value, multiply it by its probability of occurring, and you add these up...