ELI5; What are random variables and their probability distributions and what are their real world applications?
In: Mathematics
Random variables are variables that aren’t consistent or controllable and will vary slightly. They’re everywhere but personally I’m a mechanical engineer, so my examples are going to tend towards that a bit. Manufactured parts won’t be exactly what they should be. If you want a part that’s 1 inch long, you’re going to get parts that are 0.95, 1.03, 1.1, 0.98, 1.05, etc. Another example is sensor noise that can come from a bunch of sources. Let’s say, you’re measuring the windspeed in a wind tunnel. You’ll get 5.05 4.85 5.5 5.3 4.7 4.9 5.08 and so on. Typically, these can be seperated out into a mean measurement and some random noise.
The probability distribution is what describes how this random noise occurs. As an example, you can get [gaussian or normal distribution](https://images.app.goo.gl/drsFtDGjVdqWmgGr9), where numbers close to a center are more likely. Uniform distribution, where all numbers are equally likely. Or [multimode](https://images.app.goo.gl/6wZJgC5734bbpUKq6) distribution where numbers are centered around multiple peaks.
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