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Dialogue: 0,0:00:00.77,0:00:02.18,Default,,0000,0000,0000,,- [Instructor] What we're\Ngoing to do in this video
Dialogue: 0,0:00:02.18,0:00:03.91,Default,,0000,0000,0000,,is learn how to use a graphing calculator,
Dialogue: 0,0:00:03.91,0:00:05.97,Default,,0000,0000,0000,,in particular a TI84.
Dialogue: 0,0:00:05.97,0:00:08.39,Default,,0000,0000,0000,,If you're using any other TI\NTexas Instrument calculator
Dialogue: 0,0:00:08.39,0:00:10.96,Default,,0000,0000,0000,,it'll be very similar in\Norder to answer some questions
Dialogue: 0,0:00:10.96,0:00:13.41,Default,,0000,0000,0000,,dealing with geometric random variables.
Dialogue: 0,0:00:13.41,0:00:15.20,Default,,0000,0000,0000,,So, here we have a scenario.
Dialogue: 0,0:00:15.20,0:00:16.90,Default,,0000,0000,0000,,I keep picking cards from a standard deck
Dialogue: 0,0:00:16.90,0:00:19.24,Default,,0000,0000,0000,,until I get a king.
Dialogue: 0,0:00:19.24,0:00:22.03,Default,,0000,0000,0000,,So this is a class geometric\Nrandom variable here
Dialogue: 0,0:00:22.03,0:00:24.39,Default,,0000,0000,0000,,and it's important that\Nin this parentheses
Dialogue: 0,0:00:24.39,0:00:26.32,Default,,0000,0000,0000,,it says I replace the cards\Nif they are not a king
Dialogue: 0,0:00:26.32,0:00:28.86,Default,,0000,0000,0000,,and this important as we\Ntalk about on other videos
Dialogue: 0,0:00:28.86,0:00:32.76,Default,,0000,0000,0000,,because the probability of\Nsuccess each time can't change.
Dialogue: 0,0:00:32.76,0:00:36.44,Default,,0000,0000,0000,,And so we could define\Nsome random variable X
Dialogue: 0,0:00:36.44,0:00:38.74,Default,,0000,0000,0000,,this is a geometric random\Nvariable as being equal to
Dialogue: 0,0:00:38.74,0:00:42.07,Default,,0000,0000,0000,,the number of picks until we get a king.
Dialogue: 0,0:00:46.85,0:00:50.16,Default,,0000,0000,0000,,When we replace the cards\Nif they are not a king.
Dialogue: 0,0:00:50.16,0:00:52.15,Default,,0000,0000,0000,,And for this geometric random variable,
Dialogue: 0,0:00:52.15,0:00:54.01,Default,,0000,0000,0000,,what's the probability\Nof success on each trial?
Dialogue: 0,0:00:54.01,0:00:55.73,Default,,0000,0000,0000,,Remember what are the\Nconditions for a geometric
Dialogue: 0,0:00:55.73,0:00:57.24,Default,,0000,0000,0000,,random variable is that\Nprobability of success
Dialogue: 0,0:00:57.24,0:01:00.03,Default,,0000,0000,0000,,does not change on each trial.
Dialogue: 0,0:01:00.03,0:01:03.25,Default,,0000,0000,0000,,Well the probability of\Nsuccess is going to be equal to
Dialogue: 0,0:01:03.25,0:01:04.89,Default,,0000,0000,0000,,there's four kings in a\Nstandard deck of 52, this is
Dialogue: 0,0:01:04.89,0:01:07.70,Default,,0000,0000,0000,,the same thing as one over 13.
Dialogue: 0,0:01:07.70,0:01:09.95,Default,,0000,0000,0000,,So this first question is\Nwhat is the probability that
Dialogue: 0,0:01:09.95,0:01:11.96,Default,,0000,0000,0000,,I need to pick five cards?
Dialogue: 0,0:01:11.96,0:01:14.25,Default,,0000,0000,0000,,Well this would be the\Nprobability that our geometric
Dialogue: 0,0:01:14.25,0:01:17.16,Default,,0000,0000,0000,,random variable X is equal to\Nfive and you could actually
Dialogue: 0,0:01:17.16,0:01:19.77,Default,,0000,0000,0000,,figure this out by hand,\Nbut the whole point here
Dialogue: 0,0:01:19.77,0:01:21.96,Default,,0000,0000,0000,,is to think about how to\Nuse a calculator and there's
Dialogue: 0,0:01:21.96,0:01:26.12,Default,,0000,0000,0000,,a function called geometpdf\Nwhich stands for geometric
Dialogue: 0,0:01:27.70,0:01:31.10,Default,,0000,0000,0000,,probability distribution\Nfunction, where what you have
Dialogue: 0,0:01:31.10,0:01:33.56,Default,,0000,0000,0000,,to pass it is the probability\Nof success on any given
Dialogue: 0,0:01:33.56,0:01:37.72,Default,,0000,0000,0000,,trial, one out of 13, and\Nthen the particular value
Dialogue: 0,0:01:38.92,0:01:41.13,Default,,0000,0000,0000,,of that random variable\Nthat you want to figure out
Dialogue: 0,0:01:41.13,0:01:43.88,Default,,0000,0000,0000,,the probability for, so\Nfive right over there.
Dialogue: 0,0:01:43.88,0:01:45.74,Default,,0000,0000,0000,,Now just to be clear, if\Nyou're doing this on an AP exam
Dialogue: 0,0:01:45.74,0:01:48.63,Default,,0000,0000,0000,,and this is one of the reasons\Nwhy a calculator is useful,
Dialogue: 0,0:01:48.63,0:01:52.26,Default,,0000,0000,0000,,you can use this on an AP\Nexam, AP statistics exam.
Dialogue: 0,0:01:52.26,0:01:54.63,Default,,0000,0000,0000,,It's important to tell the\Ngraders if you're doing it
Dialogue: 0,0:01:54.63,0:01:56.92,Default,,0000,0000,0000,,on the free response that\Nthis right over here is your
Dialogue: 0,0:01:56.92,0:01:59.28,Default,,0000,0000,0000,,P and that this right over\Nhere is your five just so
Dialogue: 0,0:01:59.28,0:02:02.45,Default,,0000,0000,0000,,it's very clear that where you\Nactually got this information
Dialogue: 0,0:02:02.45,0:02:04.82,Default,,0000,0000,0000,,from or why you're actually typing it in.
Dialogue: 0,0:02:04.82,0:02:06.79,Default,,0000,0000,0000,,But let's just see how it\Nworks, what this probability
Dialogue: 0,0:02:06.79,0:02:09.56,Default,,0000,0000,0000,,is actually going to amount to.
Dialogue: 0,0:02:09.56,0:02:12.28,Default,,0000,0000,0000,,Alright so I have my calculator\Nnow and I just need to type
Dialogue: 0,0:02:12.28,0:02:15.69,Default,,0000,0000,0000,,in geometpdf and then those parameters.
Dialogue: 0,0:02:15.69,0:02:17.40,Default,,0000,0000,0000,,And so the place where I\Nfind that function I press
Dialogue: 0,0:02:17.40,0:02:21.92,Default,,0000,0000,0000,,2nd, distribution right over\Nhere, it's a little above
Dialogue: 0,0:02:21.92,0:02:23.85,Default,,0000,0000,0000,,the vars button.
Dialogue: 0,0:02:23.85,0:02:26.04,Default,,0000,0000,0000,,And then I click up, I can\Nscroll down or I could just
Dialogue: 0,0:02:26.04,0:02:27.68,Default,,0000,0000,0000,,go to the bottom of the list\Nand you can see the second
Dialogue: 0,0:02:27.68,0:02:31.24,Default,,0000,0000,0000,,from the bottom is\Ngeometpdf, click Enter there.
Dialogue: 0,0:02:31.24,0:02:34.72,Default,,0000,0000,0000,,My P value, my probability\Nof success on each trial
Dialogue: 0,0:02:34.72,0:02:37.40,Default,,0000,0000,0000,,is one out of 13, and I want\Nto figure out the probability
Dialogue: 0,0:02:37.40,0:02:40.81,Default,,0000,0000,0000,,that I have to pick five cards.
Dialogue: 0,0:02:40.81,0:02:44.20,Default,,0000,0000,0000,,And so then click Enter,\Nclick Enter again,
Dialogue: 0,0:02:44.20,0:02:48.08,Default,,0000,0000,0000,,and there you have it, it's about 0.056.
Dialogue: 0,0:02:48.08,0:02:50.66,Default,,0000,0000,0000,,So this is approximately 0.056.
Dialogue: 0,0:02:54.58,0:02:56.92,Default,,0000,0000,0000,,Now let's answer another\Nquestion, so here they say
Dialogue: 0,0:02:56.92,0:02:59.28,Default,,0000,0000,0000,,what is the probability that\NI need to pick less than
Dialogue: 0,0:02:59.28,0:03:00.12,Default,,0000,0000,0000,,10 cards?
Dialogue: 0,0:03:01.62,0:03:05.70,Default,,0000,0000,0000,,So this is the probability\Nthat X is less than 10
Dialogue: 0,0:03:08.02,0:03:10.42,Default,,0000,0000,0000,,or I could say this is equal\Nto the probability that
Dialogue: 0,0:03:10.42,0:03:13.08,Default,,0000,0000,0000,,X is less than or equal to nine.
Dialogue: 0,0:03:14.64,0:03:16.62,Default,,0000,0000,0000,,And I could say well this\Nis the probability that X
Dialogue: 0,0:03:16.62,0:03:19.45,Default,,0000,0000,0000,,is equal to one plus the\Nprobability that X is equal to
Dialogue: 0,0:03:19.45,0:03:23.62,Default,,0000,0000,0000,,two all the way to the probability\Nthat X is equal to nine.
Dialogue: 0,0:03:25.91,0:03:27.86,Default,,0000,0000,0000,,But that would take a\Nwhile, even if I used this
Dialogue: 0,0:03:27.86,0:03:29.54,Default,,0000,0000,0000,,function right over here.
Dialogue: 0,0:03:29.54,0:03:31.88,Default,,0000,0000,0000,,But lucky for us, there's\Na cumulative distribution
Dialogue: 0,0:03:31.88,0:03:33.97,Default,,0000,0000,0000,,function, take some space\Nfrom the next question,
Dialogue: 0,0:03:33.97,0:03:38.14,Default,,0000,0000,0000,,this is going to be equal\Nto geometcdf, cumulative
Dialogue: 0,0:03:39.80,0:03:42.67,Default,,0000,0000,0000,,distribution function and once\Nagain I pass the probability
Dialogue: 0,0:03:42.67,0:03:47.32,Default,,0000,0000,0000,,of success on any trial and\Nthen up to including nine.
Dialogue: 0,0:03:47.32,0:03:49.55,Default,,0000,0000,0000,,So let's get the calculator out again.
Dialogue: 0,0:03:49.55,0:03:53.43,Default,,0000,0000,0000,,So we go to 2nd, distribution,\NI click up and there we
Dialogue: 0,0:03:53.43,0:03:56.28,Default,,0000,0000,0000,,have it geomet cumulative\Ndistribution function, press
Dialogue: 0,0:03:56.28,0:04:00.63,Default,,0000,0000,0000,,Enter, one out of 13 chance\Nof success on any trial.
Dialogue: 0,0:04:00.63,0:04:04.05,Default,,0000,0000,0000,,Up to and including nine, and then Enter.
Dialogue: 0,0:04:05.70,0:04:09.87,Default,,0000,0000,0000,,And there you have it, it's\Napproximately 51.3% or 0.513.
Dialogue: 0,0:04:10.84,0:04:13.42,Default,,0000,0000,0000,,So this is approximately 0.513.
Dialogue: 0,0:04:16.61,0:04:17.86,Default,,0000,0000,0000,,Now let's do one more.
Dialogue: 0,0:04:17.86,0:04:20.04,Default,,0000,0000,0000,,What is the probability that\NI need to pick more than
Dialogue: 0,0:04:20.04,0:04:21.32,Default,,0000,0000,0000,,12 cards?
Dialogue: 0,0:04:21.32,0:04:22.78,Default,,0000,0000,0000,,And like I'll pause the video\Nand see if you can figure
Dialogue: 0,0:04:22.78,0:04:24.45,Default,,0000,0000,0000,,this one out, what function\Nwould I use on my calculator,
Dialogue: 0,0:04:24.45,0:04:26.65,Default,,0000,0000,0000,,how would I set it up?
Dialogue: 0,0:04:26.65,0:04:28.83,Default,,0000,0000,0000,,Well the probability, this\Nis the probability that X
Dialogue: 0,0:04:28.83,0:04:32.100,Default,,0000,0000,0000,,is going to be greater than\N12, which is equal to one
Dialogue: 0,0:04:34.97,0:04:39.14,Default,,0000,0000,0000,,minus the probably that x\Nis less than or equal to 12.
Dialogue: 0,0:04:41.83,0:04:44.81,Default,,0000,0000,0000,,And now this we could just use\Nthe cumulative distribution
Dialogue: 0,0:04:44.81,0:04:48.64,Default,,0000,0000,0000,,function again, so this\Nis one minus geometcdf
Dialogue: 0,0:04:51.29,0:04:55.45,Default,,0000,0000,0000,,cumulative distribution\Nfunction, cdf, of one over 13
Dialogue: 0,0:04:59.37,0:05:02.04,Default,,0000,0000,0000,,and up to and including 12.
Dialogue: 0,0:05:02.04,0:05:04.20,Default,,0000,0000,0000,,So what is this going to be equal to?
Dialogue: 0,0:05:04.20,0:05:09.19,Default,,0000,0000,0000,,So 2nd, distribution, I click\Nup, I get to the function.
Dialogue: 0,0:05:09.19,0:05:12.95,Default,,0000,0000,0000,,Click Enter, and so I\Nalready have that first,
Dialogue: 0,0:05:12.95,0:05:16.55,Default,,0000,0000,0000,,the probability of success on\Nevery trial is one over 13,
Dialogue: 0,0:05:16.55,0:05:21.17,Default,,0000,0000,0000,,and then cumulative up to\N12 and so I click Enter.
Dialogue: 0,0:05:21.17,0:05:24.98,Default,,0000,0000,0000,,And then well I could click\NEnter there, but I really want
Dialogue: 0,0:05:24.98,0:05:28.91,Default,,0000,0000,0000,,to get one minus this\Nvalue, so I can do one minus
Dialogue: 0,0:05:28.91,0:05:33.08,Default,,0000,0000,0000,,2nd Answer, which would be\Njust one minus that value,
Dialogue: 0,0:05:35.21,0:05:39.54,Default,,0000,0000,0000,,which will be equal to there\Nyou have it, it's about 38.3%
Dialogue: 0,0:05:39.54,0:05:40.38,Default,,0000,0000,0000,,or 0.383.
Dialogue: 0,0:05:41.78,0:05:45.94,Default,,0000,0000,0000,,So this is approximately\Nequal to 0.383 and we're done.