The geometric distribution
TI-84 geometpdf and geometcdf functions
- [Instructor] What we're going to do in this video is learn how to use a graphing calculator, in particular a TI84. If you're using any other TI Texas Instrument calculator it'll be very similar in order to answer some questions dealing with geometric random variables. So, here we have a scenario. I keep picking cards from a standard deck until I get a king. So this is a class geometric random variable here and it's important that in this parentheses it says I replace the cards if they are not a king and this important as we talk about on other videos because the probability of success each time can't change. And so we could define some random variable X this is a geometric random variable as being equal to the number of picks until we get a king. When we replace the cards if they are not a king. And for this geometric random variable, what's the probability of success on each trial? Remember what are the conditions for a geometric random variable is that probability of success does not change on each trial. Well the probability of success is going to be equal to there's four kings in a standard deck of 52, this is the same thing as one over 13. So this first question is what is the probability that I need to pick five cards? Well this would be the probability that our geometric random variable X is equal to five and you could actually figure this out by hand, but the whole point here is to think about how to use a calculator and there's a function called geometpdf which stands for geometric probability distribution function, where what you have to pass it is the probability of success on any given trial, one out of 13, and then the particular value of that random variable that you want to figure out the probability for, so five right over there. Now just to be clear, if you're doing this on an AP exam and this is one of the reasons why a calculator is useful, you can use this on an AP exam, AP statistics exam. It's important to tell the graders if you're doing it on the free response that this right over here is your P and that this right over here is your five just so it's very clear that where you actually got this information from or why you're actually typing it in. But let's just see how it works, what this probability is actually going to amount to. Alright so I have my calculator now and I just need to type in geometpdf and then those parameters. And so the place where I find that function I press 2nd, distribution right over here, it's a little above the vars button. And then I click up, I can scroll down or I could just go to the bottom of the list and you can see the second from the bottom is geometpdf, click Enter there. My P value, my probability of success on each trial is one out of 13, and I want to figure out the probability that I have to pick five cards. And so then click Enter, click Enter again, and there you have it, it's about 0.056. So this is approximately 0.056. Now let's answer another question, so here they say what is the probability that I need to pick less than 10 cards? So this is the probability that X is less than 10 or I could say this is equal to the probability that X is less than or equal to nine. And I could say well this is the probability that X is equal to one plus the probability that X is equal to two all the way to the probability that X is equal to nine. But that would take a while, even if I used this function right over here. But lucky for us, there's a cumulative distribution function, take some space from the next question, this is going to be equal to geometcdf, cumulative distribution function and once again I pass the probability of success on any trial and then up to including nine. So let's get the calculator out again. So we go to 2nd, distribution, I click up and there we have it geomet cumulative distribution function, press Enter, one out of 13 chance of success on any trial. Up to and including nine, and then Enter. And there you have it, it's approximately 51.3% or 0.513. So this is approximately 0.513. Now let's do one more. What is the probability that I need to pick more than 12 cards? And like I'll pause the video and see if you can figure this one out, what function would I use on my calculator, how would I set it up? Well the probability, this is the probability that X is going to be greater than 12, which is equal to one minus the probably that x is less than or equal to 12. And now this we could just use the cumulative distribution function again, so this is one minus geometcdf cumulative distribution function, cdf, of one over 13 and up to and including 12. So what is this going to be equal to? So 2nd, distribution, I click up, I get to the function. Click Enter, and so I already have that first, the probability of success on every trial is one over 13, and then cumulative up to 12 and so I click Enter. And then well I could click Enter there, but I really want to get one minus this value, so I can do one minus 2nd Answer, which would be just one minus that value, which will be equal to there you have it, it's about 38.3% or 0.383. So this is approximately equal to 0.383 and we're done.
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