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Suppose that the number of orders per hour at a pizza shop follows a Poisson process with rate 5 per 30 minutes. Suppose that the pizza orders are large with probability 2/3, small with probability 1/3, and the size of the pizza order is independent of the time of the call.

a) What is the probability that in 45 minutes, exactly 3 large and 2 small orders will be made?

b) What is the probability that 5 large orders will be made before 4 small orders are made?

c) Given that exactly 8 orders are made within the first hour, what is the probability that exactly 2 large and 2 small orders were made in the first half hour?

What I tried: should lambda change in terms of probability and time? Lambda will be rate 7.5*2/3 = 5 for large orders; For small orders it will be: 2.5 Am I correct?

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  • $\begingroup$ hmm... you haven't defined your $\lambda$. If you are referring to the parameter for the Poisson distribution that you are going to use then it depends on the time interval length and the event of interest. btw, add self-study tag. An attempt should include what you did. $\endgroup$ – Siong Thye Goh Sep 10 '18 at 2:52
  • $\begingroup$ @SiongThyeGoh Done! edited the post with my attempt of changing lambda. $\endgroup$ – user218970 Sep 10 '18 at 4:22
  • $\begingroup$ first part is alright. try to attempt the whole thing rather than just the front part if possible. $\endgroup$ – Siong Thye Goh Sep 10 '18 at 15:11

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