So, we have a probability of P where what is going toīe our squared distance from the expected value? Well, we're going to get a To be the probability squared distances from the expected value. Out the variance of Y, so variance of Y is going to be equal to what? Well, here it's going What is the variance of Y going to be equal be? So, let me scroll over a little bit, get a little bit of more real estate and I will figure that So, it's gonna be similarly N times the variance, N Now, we're gonna do the same idea to figure out what the variance of X is going to be equal to because we could see, we knowįrom our variance properties, you can't do this with standard deviation but you could do it with variance and then once you figure out the variance, you just take the square root for the standard deviation, the variance of X is similarly going to be the sum of the Of Y is really just P and so, if you said theĮxpected value of X, well, that's just going to be, let me just write it over here, this is all review, we could say that the expected value of X is just going to be equal to, we know from our expected value properties that it's going to be equal to the sum of the expected values of these N Ys, or you could say it is N times the expected value, times the expected value of Y, the expected value of Y is P, so this is going to be equal to N times P. This whole term's gonna be zero and so, the expected value
#0.3 times 10 plus 0.7 times 100 plus
So, it's P times one plus one minus P, one minus P, times zero, times zero. Expected value of Y is just the probability weighted outcomes. Of X is going to be because the expected value of Y is pretty straightforward
The probability that it's a failure that Y is equal to zero is one minus P, so you could view Y, the outcome of Y or whether Y is one or zero is really whether we had a success or not in each of these trials, so if you add up N Ys, then you are going to get X and we use that information to figure out what the expected value So, this variable, this random variable Y, the probability that's equal to one, you could do that as a
And we also talked in that previous video where we talked about the expected value of this binomial variable we said hey, it could be viewed that this binomial variable can be viewed as the sum of N of what you could really consider to be a Bernoulli variable here.
#0.3 times 10 plus 0.7 times 100 trial
Success is equal to P, so the probability isĬonstant across the trials for each of these independent trials, so the probability of success in one trial is not dependent on what Successes from N trials, so it's a finite number of trials where the probability of And so, like in the last video I have this binomial variable X that's defined in a very general sense. Trying to understand what the expected valueĪnd what the variance of a binomial variable is going to be or what the expected value or the variance of a binominal distribution is going to be which is just the distribution
Going to do in this video is continue our journey
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