 If we look at this then let's just I'll show you in a couple different ways. I'm going to pull this to the right I Could say let's say this is going to be x times P times P of x Brackets I'm going to make this black white centered and wrap and So I could say this is going to be Then this times this Right, I'm going to copy that all the way down So and then let's say that this is going to add. Let's add some decimals here So basically we could say in the one minute time interval, right? There's a likelihood that one person arrives We have seventeen 0.8% so that would be like 0.18% Of a person right if we were to calculate this out to try to get the mean right and if the likelihood in one minute time of two People arrive is going to be the 24.3 percent so we can say that'd be like 0.49 percent of a person so then if I if I Multiply that out and then I add up the this I'm going to equals the sum of This control shift down and I add a decimal home tab Number group adding some decimals. There's our mean so we can also calculate so you can see that's the mean that we came up to over here So we can also calculate that using a function, which is a good time to introduce We can use the sum product So if I want to do that this way I can say this equals the sum product Brackets and then I've got my two arrays because I want to multiply Then this array times this array. So I'm going to select this entire array control shift down and Then say comma the next argument or the next array is going to be this control shift down and Enter so now I should get the same thing home tab number Couple decimals now if we wanted to get to the variance we could do that a couple different ways I'm going to pull this over. I'm going to pick these two up I'm going to control X and put them over here control V and then I'll add another Column here. This column is going to be then X minus the mean And I'll pick this up and say home tab and clipboard and so now I'm going to say this is going to be X This number minus the mean which we've calculated a few different ways. Let's pull it over here I'm going to F4 to make that an absolute reference F4 and Enter and then I can add a couple decimals number group adding a couple decimals Fill handle copy that down So I'm going to take that and then I'm going to square it so I'm going to say this is going to be squared and I'll format paint this home tab paint brush Squared to do that. I'm going to say equals the cell to the left carrot shift six To to get to the power of two or squared entered I can add a couple decimals there double-click on the fill handle Bringing it down and now I'm going to take that column times the P of X times P of X and I'll put my cursor here Paint brush here, and then this is going to be equal to this That we just calculated times the P of X percent and Let's add some decimals Does some of decimalizing it double-click bringing that down and so to get to the variance one way we can do that variance is I'm going to say equals the sum of These items control shift down Enter and if I add some decimals We get to the same 2.73 because that's part of the relationship of a Poisson distribution and this is the perfect Poisson distribution now you can also do that variance calculation just to practice the some product function So we'll say this equals some product. This is an array formula I want another bracket because I'm going to take it to the power of two or square it put my cursor on Cell a b2 control shift down on the keyboard so I can go down to the bottom I'm holding control backspace so I can go back up top with the keyboard And then I want to take each of those minus the mean which I'll pick up here in AK so I'm going to pull this down and So we have that closing the brackets taking it to the power of two So I'll say shift six carrot to the power of two square in it And then the second bit comma the second array is now going to be here a C2 control shift down and then I'm going to hold control backspace to go back up to the top and Close up the brackets and enter. So there we have it. I'm going to then go to the home tab and Fonts group and add some decimals and once again, we have the variance should be the same As the means so just a little bit of practice with the excel formulas there now some other questions that we might ask From like a from like a practical standpoint is we might say we might ask What's the likelihood that we have equal to or less than three? Arrivals within a one-minute time period. These are the kind of questions we can ask now if I plotted everything out over here I could say well these this is the likelihood that zero people arrive exactly one people arrive exactly two people three people And I could sum those up. I could say okay. This is equal to the sum of these