TI-84 geometpdf and geometcdf functions | Random variables | AP Statistics | Khan Academy

What we're going to do in this video is learn how to use a graphing calculator, in particular, a TI-84. 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 classic geometric random variable. Here, it's important that in this parenthesis it says I replace the cards if they are not a king. This is important as we talk about in other videos because the probability of success each time can't change.

We could define some random variable X, which is a geometric random variable, as being equal to the number of picks until we get a king. 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, one of the conditions for a geometric random variable is that the probability of success does not change on each trial.

Well, the probability of success is going to be equal to—there are four kings in a standard deck of 52—and this is the same thing as 1 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.

You could actually figure this out by hand, but the whole point here is to think about how to use a calculator. There is a function called geomet pdf, which stands for geometric probability distribution function. What you have to pass it is the probability of success on any given trial, 1 out of 13, and then the particular value of that random variable that you want to figure out the probability for—so 5 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 actually use this on an AP exam, AP Statistics exam. It's important to tell the graders if you're doing this on the free response that this right over here is your P and that this right over here is your 5—just so it's very clear 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 geomet pdf and then those parameters. The place where I find that function: I press second distribution right over here, this little blue above the vars button, and then I can click up.

I could scroll down or I could just go to the bottom of the list, and you can see the second from the bottom is geomet pdf. I click enter there. My P value, my probability of success on each trial, is 1 out of 13, and I want to figure out the probability that I have to pick five cards. Then, I 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 9. I could say, well, this is the probability that X is equal to 1 plus the probability that X is equal to 2 all the way to the probability that X is equal to 9.

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 geo met cdf, cumulative distribution function. Once again, I pass the probability of success on any trial and then up to and including nine.

So, let's get the calculator out again. We go to second distribution, I click up, and there we have geomet cumulative distribution function. Press enter: 1 out of 13 chance of success on any trial up to and including nine, and then enter. There you have it: it's approximately 51.3 percent or 0.513. So, this is approximately 0.5.

Now, let's do one more. What is the probability that I need to pick more than 12 cards? I'll pause the video and see if you can figure this one out. What function would I use on my calculator, or 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 1 minus the probability that X is less than or equal to 12.

And now, this we can just use the cumulative distribution function again. So, this is 1 minus geo met cdf, cumulative distribution function, CDF of 1 over 13 and up to and including 12. So, what is this going to be equal to? So, second distribution, I click up, I get to the function, click enter.

I already have that first: the probability of success on every trial is 1 over 13, and then cumulative up to 12. So, I click enter. Then, well, I could click enter there, but I really want to get 1 minus this value. I can do 1 minus second answer, which would be just 1 minus that value, which will be equal to—there you have it: it's about 38.3 percent or 0.383. So, this is approximately equal to 0.383.

And we're done.