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Write for me capstone project georgia order capstone far west mining chevrolet upcoming cars in india 2018 annual report hi guys I'd like to talk about the exponential distribution and how to calculate probabilities using the exponential distribution so before we get started I'll give you guys a little bit of a background of what the exponential distribution is okay it's actually the actually closely related to the Poisson distribution so the Poisson is usually quite mandatory in most stats courses exponential it's sometimes optional get the Poisson distribution okay allows us to answer questions like this the number of events that occur in an interval time interval of time so this is what Poisson distributions help us answer okay with exponential it's like the flip side of this it's like the flip side of these type of questions okay so with exponential distribution what we'll be answering is the time taken between two events occurring all right so you can see that they're very closely related so today we're going to go through things but we're going to talk about on the exponential distribution so whenever you see a question that talks about two events occurring two things occurring so let's say a and B and they want you to calculate the time between a and B occurring then you're dealing with an exponential question now there are a few things we need to cover up quite briefly anyway so the exponential distribution looks like this you really need to draw the graph but it looks like that okay and so um on the x-axis you have time okay and so on now the parameter of interest is called lambda right and lambda is the average number of events in one unit of time okay so it's the average number of events that occur in one unit the time so what we need on one unit of time well if they're talking about minutes then it's the average number of events in one minute if they're talking about hours then it's the average number of events in one hour okay now we'll go through a web solution or work questions of this will be clearer now the other thing we need to know is the actual equations for calculating the probability so the probability that X so you know the time between two events is larger than the particular time is equal to the exponential to power of negative lambda X okay and the probability that the number that the time between two events is less than the particular number of time so small X that's equal to 1 minus exponential to the power of negative lambda X unfortunately I don't have a calculator here with me so I can't show you guys exactly how to punch that into your calculator but the button you need is your exp button okay so if I wanted to calculate exponential of five okay if I wanted to calculate this I would click on this button exp and then I'd click on five and then equals and that would give me exponential of five okay I'm lazy moment so I don't want to type this up so let's just borrow this question straight from the textbook okay a checkout counter at a supermarket completes the process according to an exponential distribution with a surface rate of six per hour a customer arrives at the checkout counter find the probability of the following events the service is completed in fewer than five minutes the customer leaves a checkout counter more than ten minutes after arriving and the service is completed in time between five and eight minutes so we have a checkout rate here oh wait we have we have some type of lambda here right that tells us per unit of time how many events or how many customers do we serve um per hour and let's have a look now the first thing you should notice is that the questions asking us about minutes okay so that's our unit of time for answering question but they've given us lambda in terms of per hour so six customers per hour so we need to convert our into minutes okay okay so what do we have what do we go alright so question a right so we're told that we see six customers but checkout person sees on average six customers per hour okay and our lambda has to be in terms of per minute okay so lambda equals two or if we see six per hour then if we want to know the per minute rate it's six divided by sixty right because it's 60 minutes one hour so lambda is equal to zero point one so that means we see zero point one customers per minute okay all right and then we just simply have to punch in our equations right so the the probability okay that it takes less than five minutes to see one customer from start to finish okay is equal to right so we just look at these equations from from before okay so we look at this equation here probably that X is less than five we just sub in x equals to five we already know lambda and that's it okay so all we have to do is we know that's 1 minus e okay so to the power of negative lambda so we know what lambda R is so it's negative zero point one okay we know what X is X is five so it's less than five minutes okay so five minutes you know in between the two events here we punch that into our calculator so unfortunately I have my calculator here with me so I can't show you guys had punch that in but it's pretty straightforward so you just need practice with that and this is it so it's a zero point three nine three five chance that we see that that we can complete the customers check out within five minutes question B alright and so the next question was on what's the probability that we see that it takes more than 10 minutes to see a particular customer so what's the probability that it takes more than 10 minutes after arriving to finish your checkout F of the time between arriving and you know completing the checkout takes more than 10 minutes well the probability that X is more than 10 right that's equal to e negative lambda X right okay and we simply have to solve our values in which is the negative K so lamb double zero point 1 and X now is 10 because we want to know 10 minutes and that gives us zero point three six seven nine okay Patsey so Part C was on what's the probability that it takes between five and eight minutes to see a to complete a customer completed customers you know um purchase at the checkout so what's the probability that it's that X is between five minutes and eight minutes okay so this is what's happening you okay now if you recall how we calculate these probabilities would just be the probability that X is less than 8 - probability that X is less than 5 okay and we can break it down to those two components and that will give us our answer now I just intuitively show you guys how we do that okay so let's say this is between zero and eight minutes okay the first term here gives me this whole distance here right between so less than eight so we know it would so this gives us a probability that takes eight minutes or less to see this customer okay the second term here let's say five is up here okay give me the area that the difference or you know the time taken which is five minutes or less which is this distance here so if I have this distance minus this distance that will leave me with this distance here between five and eight okay and that's what's happening so that's how we can break it down into these two components okay so what's the first term okay so probability that X is less than 8 is simply 1 minus e minus 0.18 okay minus the second term - okay there are two minuses here so I'm going to use a bracket so I don't get confused okay and then we can simplify this right now once cancel out that's one minus one two negatives which gives me a positive there so that would be a negative 0.15 minus E okay and the answer would be 0.15 seven - okay and so there's a 0.15 7 - chance that a check out will see a customer between five and eight minutes I hope this was helpful example capstone projects cheap Empire State College.

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