This can be given by the summation over all X of X squared times the probability mass function minus the main squared. Now for the variance on the number of that vote for the left role. And now and this comes out to a mean number voting for the left role instead of the right role of point 0004. Now, just in case you're wondering why these add up to slightly more than one. Now the mean can be given by the expected value formula, which is the summation over all X of x times the probability mass function. So now we're ready to solve for our mean and our variants. So that constitutes our probability mass function. And for all four computers, voting for the left role when the right role is appropriate, It's 10 to the -16. If we do the same thing for three computers, calling for the road to the left Comes out to four times 10 to the -12. And fortunately this is a pretty small occurrence, it's six times 10 to the -8. And if we find the permutations for these different computers, calling for the left and right roles, It's four choose to. So two computers are calling for the inappropriate road to the left, two are calling for the appropriate road to the right. Now for two computers to be calling for the road to the left, We have. And so there are four ways for one of the four computers to be the one that calls for the road to the left. So it could be the first computer, the second computer, the third computer or the fourth computer that calls for the road to the left. That would call for the appropriate road to the right. Now, for the probability that one of the four computers calls for the inappropriate role, The probability of an individual computer calling for the wrong rule is. 9999 to the exponent for And that comes out to. Is the probability that all for our successful, which is the probability that they will call for a roll to the right.
So the probability of that zero of the computers call for the wrong road to the left. So the first step is to find the probability mass function for X. And so we are asking this question what the mean? And the variance of X is. Our random variable X is the number of computers out of the four that vote for a left role when the right role is the appropriate move. When a road to the right is actually the appropriate thing to call for. And these computers can with probability Of. A space shuttle's flight is controlled by four independent computers.
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