All right. So here we're given a random variable with its probability distribution and asks us some questions about it. So for party, it wants us to find the expected value of this variable. So a at once expected value of X, which could also be written as mu of X and recall the move X equals the sum of each value. The random variable can take times f of X. The probability of it occurs. It's a weighted average. So looking at the chart, we see that you have X equals two times 0.2. Plus, there's a value of four 0.3% of the time. Plus it has a value of seven 0.4% of the time. And finally it is a value of eight, the remaining 0.1 of the time. So if you plug this into a calculator, you will find that this is 5.2. All right, So for part B, it wants us to find the variance of X, which can also be written as the standard deviation squared of X, and that is equal to have some of each of the variables values distance from the mean squared waited by the probability. So this works out to if we look at the chart again to minus 5.2 squared times 0.2 plus four minus 5.2 squared times 0.3 plus seven minus 5.2 squared times point for plus a minus 5.2 squared times 0.1. And that works out to If you have a calculator, it makes us much easier. Works out to four point 56 All right. Another last part part, See, wants the standard deviation of acts, and this is just equal to the square root of the variance. Well, charity calculated. So the standard deviation equals the square root, but 4.56 which equals about two 0.14 And if you have a T I 84 calculator, there's a really easy trick to do. Both of these just from the calculator. So put, I'll just do ah, calculator trip. Okay, so if you have a t I 84 put X into list one and put F of X into l two and make sure they're lined up properly. Then do one of our stats. L one then l, too, as the frequency list and it will tell you the mean and the standard deviation, which is really cool and saves a lot of time.