| 00:00 - 00:03 | As we can see by plotting the density function, |
| 00:04 - 00:05 | the normal distribution has mean mu |
| 00:05 - 00:07 | and variance sigma squared. |
| 00:08 - 00:12 | As the input of the pdf tends away from the mean, |
| 00:12 - 00:15 | the value of the pdf tends to 0. |
| 00:17 - 00:19 | So a normally distributed random variable is most likely to be mu |
| 00:19 - 00:21 | since mu is the unique argmax of the pdf. |
| 00:24 - 00:26 | My Fuhrer... |
| 00:27 - 00:28 | Since it's a pdf... |
| 00:31 - 00:33 | Since it's a pdf the probability of any point is 0. |
| 00:34 - 00:36 | You have to think in terms of intervals, not points. |
| 00:53 - 00:58 | Everyone who thinks this is bullshit please leave the room. |
| 01:13 - 01:15 | It can't be probability zero! |
| 01:15 - 01:17 | If all points have probability zero then nothing would happen! |
| 01:18 - 01:23 | They told me that you guys knew what you were talking about! |
| 01:25 - 01:28 | Yet here you are spouting unbelievable nonsense |
| 01:29 - 01:31 | that nobody sane would ever believe! |
| 01:31 - 01:34 | "All points have zero probability" |
| 01:34 - 01:37 | yet when I run my simulation a point shows up! |
| 01:37 - 01:40 | Does that point have no chance of occurring? |
| 01:40 - 01:42 | But sir, something can happen even if its probability is zero. |
| 01:42 - 01:46 | I don't believe this! How do you get away with saying this stuff? |
| 01:46 - 01:48 | Since the normal takes any real value, the probability of a single one is always zero. |
| 01:48 - 01:52 | I know the normal takes real values, but saying probability zero is too confusing. |
| 01:53 - 01:54 | It goes against the meaning of the word! |
| 01:56 - 01:57 | Probability means how likely something is to happen. |
| 01:57 - 02:00 | And something never happens if its probability is zero! |
| 02:00 - 02:03 | Why can't you say the probability is just really small? |
| 02:04 - 02:08 | When we went over discrete pmfs everything made sense. |
| 02:08 - 02:13 | If it were probability zero it never happened, and that was it! |
| 02:14 - 02:16 | You actually made me want to go into this for grad school. |
| 02:17 - 02:21 | But now I don't want to or else I'll lose my common sense like all of you! |
| 02:27 - 02:29 | I had dreams of being a data scientist. |
| 02:30 - 02:34 | Rolling in dough because I could code. |
| 02:34 - 02:36 | I'd make stuff in Python using chatGPT. |
| 02:41 - 02:42 | But I can't do this anymore. |
| 02:43 - 02:47 | I was so excited to learn about the exponential and gamma distributions. |
| 02:48 - 02:53 | Now I wish I could forget I ever tried. |
| 02:54 - 02:56 | That fucker Gauss had to ruin everything. |
| 02:56 - 02:59 | He had to make up this weird distribution |
| 03:00 - 03:02 | that has no practical application anywhere! |
| 03:04 - 03:07 | Don't worry, he's failing the class. |
| 03:14 - 03:16 | You've ruined me and my passion. |
| 03:19 - 03:23 | But at least if something has probability 1 then it will always happen. |
| 03:25 - 03:26 | What a relief. |
| 03:31 - 03:33 | It's like getting an integer after rolling a die. |
| 03:40 - 03:46 | It never fails to occur. It makes sense since it happens with probability 1. |
| 03:46 - 03:49 | And no one can take that away from me. |
| 03:53 - 03:56 | Fuck. |
