Problem 8. During rush hour. from 8 a. m. to 9 a. m., traffic accidents occur according to a Poisson process with a rate of 5 accidents per hour. Between 9 a. m. and 11 a. m., they occur as an independent Poisson process with a rate of 3 accidents per hour. What is the PMF of the total number of accidents between 8 a. m. and 11 a. m.

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Step-by-step explanation:

Yeah, that's probably we're dealing with two different porcelain distributions. The first entrance has an average of three per hour. And so this means for interest number one lambda is three. That's which means that the probability of why is three to the Y. E. To the negative third over white and coral. Now for our second entrance we have a mean of four per hour. This this means that lambda is equal to four. We don't find the probability that a total of three cars will arrive in a given out mm over here on the right and then write this down. Probably why? Then it's four to the Y. Times even the negative fourth over four facts. Or now it's fine. A few probabilities here. First for this first one, the probability of zero, we called zero in for Y, napoleon zero. And for a while will give us E. To the negative third. The probability of one there's going to be equal 23 E. To the negative 30. The probability of two will be nine hands E to the negative third. And then the probability of three when he put three and will also be nine halves here are the negative third. And so again we just plug in those values there to find those probabilities and I'll show you what we do with these. Let's find those same probabilities here on the right. And so the probability of zero and we plug in zero. Excuse me. That bottom should be Wife at Corona for we'll probably have zero here. There's going to be either an annual fourth. The probability of one, there's going to be four, even the 94th. The probability of two, it's going to be eight E 92 4th. Then the probability of three is going to be 32/3, even the negative fourth. So I found the probability of zero through three cars coming in for all of these values. Now we want exactly three to come in now. Exactly three. We mean we could have zero here and three on the right. So as you're on the left and three on the right. And so since they are independent events, you multiply those together. Each of the negative third times 32/3 to the negative third is 32/3 U. To the negative seventh. Now, another possibility is one on the left and two on the right. So multiply those together because it's 24 either the negative seven, we're gonna have to on the left and one on the right. And so we multiply those two values together and that gives us 18. Either the negative summer. And then lastly we could have three from the left and zero from the right. And so we multiply those together, Oculus nine have the to the negative seven. So we're going to add all these values together. So 32/3 plus 24 plus 18 plus nine over to gives us 3 43/6, either the negative seven and this is approximately 0.5 21

if the pizza is divided equally into 2 equal halves then you would get

πr^2/2

where r is the radius of the pizza.

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