The sign rule and continuous probability distributions | Probability and Statistics | NJ Wildberger

We describe the sign rule, which is a simple way of approximately determining when a given result from a binomial distribution is likely or not. Then we introduce continuous probability distributions, starting with measurements which take on a continuous range of values rather than a discrete collection. The mean, variance and standard deviation of a continuous probability distribution are defined analogously to discrete probability distributions, with sums replaced by integrals.

A simple example is the uniform distribution on an interval; the most important example is the normal distribution.

Video Contents:
00:00 Introduction
09:22 The sign rule [example on corn yields]
20:25 Continuous probability distributions
28:18 Continuous analog of the discrete type of probability distribution
30:30 The uniform distribution
33:57 Mean and variance for a continuous random variable
42:26 Transformation formulas
46:36 The normal distribution

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[ali]

Dear Dr. Wlidberger,
Thank you for your excellent lectures.
I have followed your lectures on Prob and Stat series up to and including # 7, the sign rule. Somehow I could not locate the last one in that series, the # 8. I am also interested to watch and take notes of your other videos. They are scattered in youtube and hard to follow them in an organized sequence. Would you please tell me if there is a web side with all your lectures in one place and if there is such a thing, would you provide me with its address? Thank you

[Alex-bmkp]

I know I should have posted on the previous video but ... is there anywhere I could get a more in-depth (for dummies) explanation of the probability generating function?

[liadorel]

Does it make sense, for a continuous density function p(x), to talk about
the probability of a specific value of x?

[mathematical_ocean]

The logic for the argument that Sue’s coach made a difference is a bit muddled because it uses “data” that didn’t happen, i.e., that Sue won 13, 14, or 15 matches. A better strategy would be to use Bayes’ rule to compute the probability of p given that she won 12 matches out of 15 and then find the mean and variance of the posterior probability distribution for p. To decide if the coach made a difference we should compare the mean of the estimated p to 0.6 to see if it is bigger by a significant amount, where significant is measured relative to the standard deviation of p.

[wgregor]

It is not true that the density p(x) has to be less than 1. In fact, p(x) can be very large. If you have a uniform distribution on the interval [0, 0.001], then p(x) = 1000 on all the interval.

[Davewoh]

Why do you look at 12 matches OR MORE, 14 +'s OR MORE?  Why not have those numbers in the middle of a range instead of as the lowest element?