WEBVTT Kind: captions; language: en-us NOTE Treffsikkerhet: 87% (HØY) 00:00:00.000 --> 00:00:07.699 In this video I want to show you how to use the online apps for simulated coin tosses and 00:00:07.699 --> 00:00:15.200 probability calculations. You can reach the apps by clicking on the links in Canvas. NOTE Treffsikkerhet: 90% (HØY) 00:00:19.800 --> 00:00:29.600 This is the coin toss simulator and it shows you results for 100 simulated people tossing a coin 00:00:29.600 --> 00:00:31.700 10 times each. NOTE Treffsikkerhet: 91% (HØY) 00:00:31.700 --> 00:00:39.650 If you want to run the same simulation again, that is a different simulated set of a hundred people 00:00:39.650 --> 00:00:44.200 tossing a coin 10 times each, you just click on toss. NOTE Treffsikkerhet: 91% (HØY) 00:00:44.200 --> 00:00:51.900 And you can do this as many times as you like to see how different the result can be from simulation 00:00:51.900 --> 00:00:53.800 to simulation. NOTE Treffsikkerhet: 87% (HØY) 00:00:55.200 --> 00:01:02.900 If you want to try a different number of simulated people, you can use this slider. Which can go from 00:01:02.900 --> 00:01:05.800 five people throwing a coin NOTE Treffsikkerhet: 82% (HØY) 00:01:05.800 --> 00:01:13.250 up to 1000 people throwing coins. NOTE Treffsikkerhet: 91% (HØY) 00:01:13.250 --> 00:01:16.000 And the number NOTE Treffsikkerhet: 91% (HØY) 00:01:16.600 --> 00:01:25.000 of times each person flips a coin, can be set using this slider. So each person can toss a coin 00:01:25.000 --> 00:01:31.300 five times or hundreds of times up to a thousand times each. NOTE Treffsikkerhet: 91% (HØY) 00:01:31.500 --> 00:01:39.700 So here is 100 simulated people tossing, a coin 100 times each and we can run more simulations with 00:01:39.700 --> 00:01:41.650 the same settings. NOTE Treffsikkerhet: 89% (HØY) 00:01:41.650 --> 00:01:51.600 In addition to the histogram of the results we can show the density curve Which approximates the 00:01:51.600 --> 00:02:01.000 envelope of the histogram, like a smooth version of the distribution of tosses or we can show the 00:02:01.000 --> 00:02:07.300 theoretically expected proportions. This is called the binomial distribution and is the 00:02:07.300 --> 00:02:10.949 mathematically expected proportion for a hundred NOTE Treffsikkerhet: 89% (HØY) 00:02:10.949 --> 00:02:16.850 people throwing a hundred coins each or a coin hundred times each. NOTE Treffsikkerhet: 89% (HØY) 00:02:16.850 --> 00:02:23.700 You can also choose to show the corresponding normal distribution, which for these settings is 00:02:23.700 --> 00:02:28.550 essentially identical to the binomial. So you cannot see them as very different. NOTE Treffsikkerhet: 91% (HØY) 00:02:28.550 --> 00:02:35.899 If you choose a lower number of coins, then you will see the difference between the binomial curve 00:02:35.899 --> 00:02:39.000 and the normal distribution. NOTE Treffsikkerhet: 91% (HØY) 00:02:39.300 --> 00:02:43.500 You can see it here very clearly. NOTE Treffsikkerhet: 91% (HØY) 00:02:45.400 --> 00:02:51.600 The second app, the online probability calculator. NOTE Treffsikkerhet: 87% (HØY) 00:02:53.200 --> 00:03:01.850 Requires you to choose a value, along the horizontal axis. So a Z value essentially. NOTE Treffsikkerhet: 91% (HØY) 00:03:01.850 --> 00:03:08.950 And then it shows you the corresponding probability for the area of your choice. NOTE Treffsikkerhet: 82% (HØY) 00:03:08.950 --> 00:03:16.500 So now Z is set to 0. We can use this slider to choose other values of Z. NOTE Treffsikkerhet: 83% (HØY) 00:03:17.200 --> 00:03:22.700 This is for a value of Z equals to 1.1 NOTE Treffsikkerhet: 88% (HØY) 00:03:22.700 --> 00:03:28.150 And we can choose to see the area for Z. NOTE Treffsikkerhet: 69% (MEDIUM) 00:03:28.150 --> 00:03:39.100 Greater than one point one, which corresponds to a probability of 13.6% or up to that value, which is 00:03:39.100 --> 00:03:46.400 the remaining probability of eighty six point four percent. We can choose to see the area between 00:03:46.400 --> 00:03:53.900 -1.1 and +1.1 or the area outside and every time we get the corresponding 00:03:53.900 --> 00:03:55.450 probability here. NOTE Treffsikkerhet: 72% (MEDIUM) 00:03:55.450 --> 00:04:01.800 What if you want to see the probability for Z equals exactly one? NOTE Treffsikkerhet: 91% (HØY) 00:04:04.400 --> 00:04:08.850 So, the display automatically updates. NOTE Treffsikkerhet: 91% (HØY) 00:04:08.850 --> 00:04:16.649 And you can see that there is a probability of about 32 percent outside one standard deviation. 00:04:16.649 --> 00:04:19.399 That's what Z equals 1 means. NOTE Treffsikkerhet: 70% (MEDIUM) 00:04:19.399 --> 00:04:28.300 And 68%, approximately 68%, inside. So you can use any number you like. What if this slider doesn't 00:04:28.300 --> 00:04:34.400 stay at the number you want? Let's say you want 1.3, but the slider won't stay there. It goes from 00:04:34.400 --> 00:04:37.799 1.29 to 1.31. NOTE Treffsikkerhet: 82% (HØY) 00:04:37.799 --> 00:04:45.450 Then you can switch to the field setting, then you can set this to be exactly what you want. NOTE Treffsikkerhet: 91% (HØY) 00:04:45.450 --> 00:04:54.100 You can even type in using the keyboard. You can type your own numbers. Exactly how much you want. NOTE Treffsikkerhet: 91% (HØY) 00:04:55.100 --> 00:04:58.800 And the rest works in the same way. NOTE Treffsikkerhet: 91% (HØY) 00:04:58.800 --> 00:05:01.900 If you want to NOTE Treffsikkerhet: 91% (HØY) 00:05:01.900 --> 00:05:05.000 move into the graph. NOTE Treffsikkerhet: 91% (HØY) 00:05:05.000 --> 00:05:11.200 So that you can see more detail. You can use this slider to change the range of the horizontal axis. 00:05:11.200 --> 00:05:14.150 So now it goes from minus 3 to 3. NOTE Treffsikkerhet: 91% (HØY) 00:05:14.150 --> 00:05:18.300 Now, it goes from minus 2 to 2. NOTE Treffsikkerhet: 78% (HØY) 00:05:19.100 --> 00:05:25.600 And later in the course you will be able to choose other distributions here to see probabilities 00:05:25.600 --> 00:05:28.100 associated with them.