00:01
Two coins are going to be flipped.
00:02
We will call them coin a and coin b.
00:07
So coin a will land on heads with probability 0 .6.
00:13
So it could be heads or tails, probability 0 .6 and 0 .4.
00:19
Eds b, heads and tails, probability 0 .7, 0 .3.
00:25
We want to find the expected value and variance of x, the total number of heads.
00:31
Okay, so there's something very helpful here.
00:35
The expected value of a plus b is equal to the expected value of a plus the expected value of b.
00:45
So we don't have to combine these, we can just find them separately and add them up.
00:50
Similarly, for variance, variance of a plus b is equal to variance.
00:56
Of a plus variance of b.
00:59
So the first equation here for mean doesn't require them to be independent, but the second one does.
01:06
You cannot add up the variance unless they are independent.
01:09
Luckily, these are.
01:11
So let's go ahead and find the means and standard deviations for these two coins.
01:16
The mean of a distribution you get by taking each possible value, multiplying it by its probability, adding them up...