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Port and Crows supporters arrive at Adelaide Oval as independentPoisson processeswith ratesλandμper minute respectviely. LetXandYbethe random number of Portan...

Question

Port and Crows supporters arrive at Adelaide Oval as independentPoisson processeswith ratesλandμper minute respectviely. LetXandYbethe random number of Portand Crows supporters entering per minute.Determine the pmf for the total number ofarrivals perminute,X+Ystarting from the law of total probability.

Port and Crows supporters arrive at Adelaide Oval as independent Poisson processeswith ratesλandμper minute respectviely. LetXandYbe the random number of Portand Crows supporters entering per minute. Determine the pmf for the total number ofarrivals per minute,X+Ystarting from the law of total probability.



Answers

During a certain part of the day, the time between arrivals of automobiles at the tollgate on a turnpike is an exponential random variable with an expected value of 20 seconds.
Find the probability that the time between successive arrivals is more than 60 seconds.

In the case of for number 110 we have a new equation of four to the x Times e to the negative fourth that foreign this for related all divided by X factorial. And so our first task is toe plug in. Um, remember five for X X is equal to five. So that means we have four to the fifth power times e to the negative fourth. So you should do that on your calculator first for the fifth time, Z Then I get 1/4 get an answer and divide that answer by five factorial. So you'll find the factorial button under the math button on your calculator, Um, or the prb it depending on what? Calculator using And you're going, Teoh, look for the exclamation point. So if you're in a t I 84 or whatever, you're gonna press math and there over to the probability so right, arrow over to probability P. R o b. And you'll find the factorial expiration point down on their otherwise look for on your T I thirties. You're gonna look for PRB button press, the pier B button and your factory buttons there. So either I go get your factory button, press enter and we're going around the nearest three decimal places. That's gonna be approximately 30.156 Then for part B. It says when a Prague in eight now for X. So that's gonna be four to the eighth Power times, even the negative fourth. When do that on your calculator first, get an answer so four to the eight times E to the negative. Fourth, get an answer and divide by eight factorial using the same ah, directions, I said before math button or the probably. But then find the factorial exclamation point. And when you press enter and get your expedition point, you're gonna get 0.0.30 approximately.

If they're three crawls for Blue Jays in five stallion's. So the three close for Blue Jews E in five standings and five s giving us a total of 12 beds. What is the probability that this bed's sited according to? So it means that that they're close these 3 50 million ways off again, Bill and, uh, Jerry pulls the four pictorial ways of arranging them and sell ings there. Five Victorio ways off, arranging them, then arranging the different. The three different breads is three Victoria and then that's the successful outcome. And then we divided by the, uh then we divided by, ah, arranging 12 beds. So our engine 12 beds in and always 12 Victoria. So this will give us, uh, one what? 62 nd which will be two points 1645 times 10 to the color Negative for

In this question, we are given ah poll redistribute probability distribution and we've given it in a table so we don't need toe do are in table So we have a value of X on picks the values of x 10 11 12 That scene on 14 on our probability X there's no point full no point to no point to again no 0.0.1 and not what one again. So we are asked to find the main and standard deviation. So to find the mean wings do x times p x So 10 times no point for is full 11 times No point to is 2.2, 12 times not 20 is to print full, sir scene times no point Well is 1.3 I'm 14 times no 140.1 is one point false. Remember, we're times ing these numbers by these so you just go down in the on So we get over, I use off x p x. And to get the mean we need our total so far probabilities, they total two bomb. So for this we need to some although things in this road. So we're gonna have four plus 2.2 plus 2.4 plus 1.3 plus 1.4, which gives us a total of 11 0.3. So this no the expectation of X which is also known as to me. To get the standard deviation, we'd first get variants and get variants. We first need to know X squared times p of x. So turn squared is 100 and 100 times about 1000.4 is 40 11 squared is 121 121 times. No point to 24 went to twelves Grad is 144. That time is not point to is 28 point eight the teens were This is a good test of your times. Tables 169 and that time is not quite one is 16.9 with 14 squared is 196 and that times 0 00.1 is 19 0.6. So now Justus, we did above. We need to get our total. So in two out of 40 24.2, 28.8, 16.9 onda 19.6. And if we some of those together with 129 0.5. So now in remember that the variation of X is the expectation of X squared, which is this number head minus expectation of X, which is all mean and we square it. So we've got 129.5 minus 11.3 squared on 11.3 squared is a home trying to 7.6 knowing I'm gonna put 11.3 squad Just remind you where I got that number from. So now we need to do that hunk in 29.5. Take away 127.6 night and we get a variation of 1.81 So last you need to do is look, that stunt innovation is the root variance. So we need to root. Need to root. Ah, one point eight. Well, on this comes out as one point three for five to three decimal places on that, it just

In discussion here were recorded that if we have the X follow the exponential, then we have the That's the it would equal to the guy each of the minus k x x greater than zero where we have the e on the expensively equity one of okay. And now in this question here, where are given X will be the time between arrivals and it follows the exponential here with the main equal to 20 seconds. So it means that with the mean here we have the e on the X, they will you go to the 20 also by the formula. It will get you one of a day and this implies. Then there came a sequel to one of a 20. Therefore, we will have that. That's the F X equal to 1/20 each. The Manus X over 20 x greater equity zero. Now want to find a probability than the time between arrival will be greater than 10 seconds. Andi, smaller than the 30 seconds and therefore this probability will be equal to the X will be smaller than 10 on bigger than 10 and smaller than the 30 with the density function. Yeah, we can register into the integral from 10 to the 30 one. Number 20 able minus X number 20 The X and began the untidy riveted on this one. E Coachella minus a djellaba minus X number 20 from 10 to 30. Everyone the 30 inside We got ego June the minus E minus three at the two. And then plus attendance that we have the mind able months and a half How we can register them into the e Bella minus half minus able minus three out with you and this will be the probability we're looking for.


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