This question covers means and standard deviations of random um Random variables in a context, in this case it's Major League Baseball and how to apply that. Um In terms of calculating the population um mean and standard deviation. So we're given that there's two types of arab bolsters X and why, and I'd like to think of X as the population variables says population related and um why as a random variable? So like random sampling. Yeah, so for the first part were first asked to find what the mean of the random variable um is and what its standard deviation is. To recall that for a mean, the formula is some of the respective values times the probability. So the probability in this case the probability is the relative frequency. Um You notice that the add up to one, so really relative frequency is just equivalent to probability. Um Then we use that information to find the standard deviation, which is the square roots of the variable squared times the probability minus the mean squared. So yeah, let's get started. Um mu of y Mhm is equal to four times points to Right, four times point to plus five times 0.23 plus six times 0.22 plus seven times 0.35 Okay. Right. And our value that we should get Um is 5.72. Yeah, And since we're talking about a number of games here, it's 5.72 games. Don't forget to include what's your variable is then from this we can find the standard deviation of the variable which is the square roots four squared times about 25 squared times 0.23 plus six squared, that's 60.22 plus seven squared Times .35 minus the music. Where Um you that we got 5.72 squared. And what we should get from here is about 1.14 um 09 games Dan. for part two be. We want to consider um what how to find uh X verbals, given why we know that, we know that. Why is the mean of the mean and standard deviation of um random variable? But what is X, X. Is the population right? And were given a random sample, But if we take sufficient, why are mean is going to be equal to the population? And so is the standard deviation right? We take a sufficiently large sample, our distribution is going to look close to the population. So in that in that case we should expect that for X or the population, the total number of games in the world series to equal to why, Which is 5.7 two games, right? We should also expect that the standard deviation is also the same, so it's also one point um 1409 games. Yeah, you should we should expect them to be the same because um the random sample uh we're taking large enough samples, it approximates the population. We should expect them to be equivalent.