But we're given this table of probabilities, and we're gonna be answering some questions about it. The first is this discreet. So the difference between discrete and continuous is that discreet only covers numbers like let's say, 012345 or 0.1 point two point free. Right. There's an infinite number of numbers in between all of these numbers that we're skipping over. So we go from 1 to 2 to free. But there's no 1.5. There's no 1.4, So this is discreet because we're not considering every single number possible. So yes, so to draw hissed a gram of the distribution, we're just going to put the points and order. We don't rearrange them from least to create IST or anything like that. And her ex access is all of the X values. So one through seven, so 567 and ah, label some points on here. So 0.2 I'll have a 0.5 a 0.1. That way we can guess a little bit a 0.2 and a point free, so one goes up. The 10.22 goes up to slightly higher than point free. Furry goes up 2.28 Cell around here four goes up two point wine, five goes up 2.5 and six and seven go up. 2.0 chill. So that's it. Find the mean and standard deviation because we're given a table. This is gonna take a whole lot longer. What we're gonna dio to find the mean is we're gonna take each x value, and we're going to multiply it by the respective probability and then add all of them up. That's what this equation here means. So to find our mean, we are going tohave one times 10.2 plus two times point free free plus free times 0.28 plus four times point wine plus five times 50.5 plus six times 0.2 plus seven times 70.2 down. If we add all of this up, you should get 2.61 Now to find the standard deviation, we're gonna need the variance and the do variance. We're gonna do the same thing for mean, but we're gonna square all of the exes and then subtract r means squared at the end. So to find variants. This time we're gonna have one square times 10.2 plus two squared at times point free free plus free squared times 20.0.28 plus four square times 40.1 plus five square times 50.5 was six square, two times 20.2 plus seven square, two times 20.2 and then we're going to take this whole fame and subtract 2.61 squared. And when we do that, we get our variance is 1.7779 and then finally, to find our standard deviation. We just take the square root of variance and you should get one point free, free, free and we are done.