1 00:00:03,870 --> 00:00:09,870 A random variable is a way to mathematically express steady acoustic outcomes as real numbers. 2 00:00:10,230 --> 00:00:15,990 So a random variable is really a functional mapping that maps a set of experimental outcomes, such 3 00:00:15,990 --> 00:00:19,980 as rolls of dice to a set of real numbers, such as one, two, three. 4 00:00:20,800 --> 00:00:24,120 So we can mathematically write this using this equation here. 5 00:00:24,570 --> 00:00:32,610 Now, this X here, this is the random variable and we can write it saying that it is a mapping between 6 00:00:32,610 --> 00:00:36,960 the set of possible outcomes s and a set of real numbers. 7 00:00:37,890 --> 00:00:41,410 Now, when we say real numbers, we can mean continuous numbers. 8 00:00:41,430 --> 00:00:44,480 So it could be any number along the number line. 9 00:00:44,520 --> 00:00:46,710 So any fractional number, any hole number. 10 00:00:46,710 --> 00:00:49,650 So it could be one point one, three point one. 11 00:00:50,610 --> 00:00:52,620 So it's just a continuous spectrum of numbers. 12 00:00:53,220 --> 00:00:55,650 It could also be a discrete set. 13 00:00:55,650 --> 00:00:59,010 So it could be integer values such as one, two, three. 14 00:01:00,470 --> 00:01:07,070 We can put this into more of a concrete concept by let's looking at an example, so let's let expe the 15 00:01:07,070 --> 00:01:09,240 random variable for a toss of the dice. 16 00:01:09,770 --> 00:01:15,710 So in this case, this is going to be a different outcomes when may roll the dice, we can get one, 17 00:01:16,010 --> 00:01:19,980 two, three dot all the way up to six dots showing on the up face. 18 00:01:20,580 --> 00:01:22,950 So these are the different outcomes of the experiment. 19 00:01:23,780 --> 00:01:27,520 Now, we have no real numbers you want to represent as the outcome. 20 00:01:27,560 --> 00:01:34,130 So this is going to be this great set and the set of set for is just going to be one, two, three, 21 00:01:34,130 --> 00:01:35,000 four, five. 22 00:01:35,570 --> 00:01:41,950 And basically what the random variable is doing, it's just going to map the outcomes to the real numbers. 23 00:01:41,960 --> 00:01:49,190 So obviously for convenience, say we're going to map the one to number one, we're going to map two 24 00:01:49,190 --> 00:01:53,880 dots to number two, and they're going to go through and do that for all the different outcomes to all 25 00:01:53,880 --> 00:01:55,070 the different discrete numbers. 26 00:01:55,970 --> 00:01:58,550 Now, there's no reason why we couldn't have this map the other way. 27 00:01:58,550 --> 00:01:59,390 We could have done it. 28 00:01:59,810 --> 00:02:03,230 We could have set a single dot is six. 29 00:02:03,860 --> 00:02:05,150 Two dots is five. 30 00:02:05,150 --> 00:02:06,370 We could have done it in reverse order. 31 00:02:06,410 --> 00:02:07,600 It doesn't matter. 32 00:02:07,750 --> 00:02:08,420 Doesn't matter. 33 00:02:08,420 --> 00:02:10,820 It's just the way that we've used to express the mapping. 34 00:02:12,950 --> 00:02:18,050 So the random variable X has a possibility of being any of the real numbers in a. 35 00:02:19,580 --> 00:02:25,940 Once the experiment is run, i.e., we toss a dice or we flip the coin once it has been carried out, 36 00:02:25,940 --> 00:02:29,820 then the value of the random variable or outcome has been determined. 37 00:02:31,070 --> 00:02:33,140 So if we roll the dice, we don't know what's going to be. 38 00:02:33,320 --> 00:02:36,590 But once it lands, then it becomes the number, it becomes the outcome. 39 00:02:36,620 --> 00:02:42,830 So in this case, it becomes five once it's become Disvalue five, once the outcome has been determined 40 00:02:43,100 --> 00:02:46,980 that it is the random value as just a normal algebraic value. 41 00:02:47,630 --> 00:02:52,850 So it's only it's only non-deterministic before the experiment is run. 42 00:02:52,940 --> 00:02:57,590 Once the experiment is run, the value becomes set and it becomes deterministic and we can just treat 43 00:02:57,590 --> 00:03:01,220 it like any other variable in an equation.