All language subtitles for 011 Continuous Distributions The Students T Distribution_en

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Would you like to inspect the original subtitles? These are the user uploaded subtitles that are being translated: 1 00:00:03,060 --> 00:00:04,110 -: Hello folks. 2 00:00:04,110 --> 00:00:05,400 In this lesson, we are going to talk 3 00:00:05,400 --> 00:00:09,357 about the student's T distribution and its characteristics. 4 00:00:09,357 --> 00:00:13,470 Before we begin, we use the lowercase letter T 5 00:00:13,470 --> 00:00:16,200 to define a student's T distribution, 6 00:00:16,200 --> 00:00:19,080 followed by a single parameter in parenthesis, 7 00:00:19,080 --> 00:00:20,823 called degrees of freedom. 8 00:00:21,780 --> 00:00:23,040 We read this next statement 9 00:00:23,040 --> 00:00:27,570 as variable Y follows a student's T distribution 10 00:00:27,570 --> 00:00:29,403 with three degrees of freedom. 11 00:00:30,750 --> 00:00:32,369 As we mentioned in the last video, 12 00:00:32,369 --> 00:00:34,740 it is a small sample size approximation 13 00:00:34,740 --> 00:00:36,695 of a normal distribution. 14 00:00:36,695 --> 00:00:40,200 In instances where we would assume a normal distribution, 15 00:00:40,200 --> 00:00:42,990 were it not for the limited number of observations, 16 00:00:42,990 --> 00:00:45,716 we use the student's T distribution. 17 00:00:45,716 --> 00:00:49,440 For instance, the average lap times for the entire season 18 00:00:49,440 --> 00:00:53,190 of a Formula One race follow a normal distribution. 19 00:00:53,190 --> 00:00:54,561 But the lap times for the first lap 20 00:00:54,561 --> 00:00:57,180 of the Monaco Grand Prix would follow 21 00:00:57,180 --> 00:00:58,803 a student's T distribution. 22 00:01:00,510 --> 00:01:03,030 Now, the curve of the student's T distribution 23 00:01:03,030 --> 00:01:06,078 is also bell-shaped and symmetric. 24 00:01:06,078 --> 00:01:09,300 However, it has fatter tails to accommodate 25 00:01:09,300 --> 00:01:12,391 the occurrence of values far away from the mean. 26 00:01:12,391 --> 00:01:16,260 That is because if such a value features in our limited data 27 00:01:16,260 --> 00:01:18,860 it would be representing a bigger part of the total. 28 00:01:20,490 --> 00:01:23,280 Another key difference between the student's T distribution 29 00:01:23,280 --> 00:01:27,030 and the normal one, is that apart from the mean and variance 30 00:01:27,030 --> 00:01:29,340 we must also define the degrees of freedom 31 00:01:29,340 --> 00:01:30,513 for the distribution. 32 00:01:32,940 --> 00:01:34,440 Great job. 33 00:01:34,440 --> 00:01:37,080 As long as we have at least two degrees of freedom, 34 00:01:37,080 --> 00:01:41,043 the expected value of a T distribution is the mean, mu. 35 00:01:42,120 --> 00:01:44,550 Furthermore, the variance of the distribution 36 00:01:44,550 --> 00:01:46,770 equals the variance of the sample, 37 00:01:46,770 --> 00:01:49,500 times the number of degrees of freedom, 38 00:01:49,500 --> 00:01:52,473 over degrees of freedom minus two. 39 00:01:54,101 --> 00:01:56,730 Overall, the student's T distribution 40 00:01:56,730 --> 00:01:59,793 is frequently used when conducting statistical analysis. 41 00:02:00,818 --> 00:02:04,320 It plays a major role when we want to do hypothesis testing 42 00:02:04,320 --> 00:02:05,153 with limited data, 43 00:02:05,153 --> 00:02:06,900 since we also have a table summarizing 44 00:02:06,900 --> 00:02:09,333 the most important values of its CDF. 45 00:02:12,120 --> 00:02:15,330 Great. Another distribution that is commonly used 46 00:02:15,330 --> 00:02:18,783 in statistical analysis, is the Chi-squared distribution. 47 00:02:19,668 --> 00:02:23,040 In the next video, we will explore where we use it, 48 00:02:23,040 --> 00:02:25,593 and what other distributions it is related to. 49 00:02:27,390 --> 00:02:28,443 Thanks for watching. 3922

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