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$$ \begin{array}{|c|ccc}{x} & {5} & {7} & {9} \\ \hline P(x) & {0.6} & {0.8} & {-0.4}\end{array} $$

Okay. We won't walk through the process of finding, um, the center of Mass, um, of a given system of point masses. And what I'm gonna do is I'm gonna go ahead and put these in the corn. It plain. So here is the cornet playing and make sure I have enough here, okay? And so the first point mass is at two three. So there is my first point mass. And that point mass is, um, a value of 12 and is at 23 Then I have one at negative one five. And so that point mass is six. And he's that negative. 15 Then I have 1/3 1 at 68 and I believe eight was a here. And that point Mass is four and 1/2 and occurs at 68 And then I have a point mass of 15 at two. Negative too. So there are my four point masses, and, um so just start finding the center of mass. I need the total mass, so we'll just take each of the masses and add them together. And so I get a total of 37.5, Then I want to find the moment about the why axes. So I want how, um, each of these point masses or distributed about the vertical axis, so that's gonna be dependent upon how far they are from the Y axis in the ex direction. So, um, the moment in the Y axis to pin him at the Y axis is each of the point masses times their respective X values. So we take each of the point masses and multiply and by the respective X values. And when we do that, we get a value, uh, 75. Then we're gonna find the moment about the X axis. And so, if I'm looking about at the moment about the X axis, I'm trying to see how these point masses are arranged about this X axis. So that's gonna be dependent upon their why value. And so my take each of the masses and multiplying by the respective why values? Um, because that's gonna be their distance away from the X axis. And then when we do that, we get a total or combined of 72. And so to find the, um X coordinate at the point mass, it is going to be the moment about the Y axis over the total mass. Um, so we get 75 over 37.5, which gives me a two to find. The Y coordinate is the moment about the X axis to buy by the total mass, which is going to give me 72 over 37.5, which becomes 48 over 25. So my center of mass is going to be two comma, 48 over 25. And so let's go ahead and taught him in. And so that means 48 over 25. So it's at two comma, just a little over two would be 50. So it's just a little under two, so right, right there.

Okay to finalise common denominator of these three for actions or expressions. So for someone to start by just taking a look of the denominator and back during them. So with this, if I fact id the denominator, I'll have 12 and then peed plus five. If I factor this denominator, I'll have P Times quantity People's five. Then for this one, I'm gonna have P plus five times people's five. So basically, I'm gonna look and see what I'm missing from each one. So I know that I have to have two factors of people's five and then I know I need a P a. Many No, I need a 12. Therefore, my lease common denominator is gonna be 12 times p times People's five times People's five.

So for this 63 9 cancel out to seven. And I just have to subtract the value of the powers if we have the same base. So six minus four is too. So I have r squared three minus two is one. So I've asked the first power, which just s 72 6 Cancel out to 12. The art. There's no Mars on the bottom. So I'm just gonna rewrite that as squared minus over s as times as over s cancel them out. We're left with one s. So then you can see that this and this are the same. So we just have to work with the coefficients. So seven minus 12 is negative five, and I just have to tack on that.

Low. Today we will be one skin continuing our discussion of probability distributions with an example of a distribution and will be determining if it is a probability is a a probability distribution or not. Now, to start with will be reviewing again. What a probability is region is. Definition is that it's a table or an equation that links each outcome of a statistical experiment with its probability of occurrence. And to determine if we're looking at probabilities is to be sure not. We have two rules number one all probabilities and the probability distribution must be between zero and one can have a negative can have anything greater than one cause then, well, they're not probabilities anymore. And number two, the sum of all over probabilities must equal one. Sorry, guys, only fix that. There we go. Now are probability that our distribution that we will be looking at today is it swallows. You have our X over our probability of X and our exes for today are three, 69 and one. Yeah, Eleanor probabilities are 0.3 0.40 point 30.1. The first things first we see that rule number one is being followed. We don't have any negative probabilities. And we don't have any probabilities greater than one. Now, for number two, Rule number two, we need our total to be equal. The one and we're gonna need to calculate that out. Now we have 0.3 plus point for 0.7. Wait three plus 30.1 to your 0.4. So, unfortunately, our total today it's 1.1 which does not equal one.