Probability & Statistics w2 - Variance in Skew lecture notes calculated incorrectly?

Shouldn’t Variance by divided by 2?

Sorry if this is just shorthand to save time… I know dividing by N doesn’t change the core point here – just wondering for correctness’ sake.

Actually I’m even more confused now:

Shouldn’t Variance = 1/n * sum (xi-mu)^2? Is the math in the screenshot just skipping steps or something?

Hello, @himmat1,

The slide’s equation can be deduced from your equation. See if you find the following make sense. Let’s consider the left case:

  1. Your mu, by the slide, is zero.

  2. Your xi, by the slide, is either -1 (lose) or 99 (win)

  3. For this part, I will leave part of the answer as your exercise :wink: , but feel free to ask if you need more hint! So, your N means the number of samples, right? The slide does not have that number, but it has the chances of lose and win, how would you convert that chance into number of samples? Let’s say, if we have 1000 samples, we have 1% chance to win, which is 10 wins, and we have 9900 loses. What would you write down according to your equation? And can you deduce the slide’s from yours?


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Hi @himmat1,

Good question! While it’s true that the formula for variance is \frac{1}{N} \sum (x_i - \mu)^2 , in this context, the expected values and variances are simplified due to the small number of outcomes. The calculations directly consider the probabilities and outcomes to handle the concept efficiently. For more accurate calculations in larger datasets, the full formula should indeed be used.

Hope this explanation helps!

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