Book 1. 20220808. Section 3.3.4.

[Rajon010]

That equality does not hold. Consider the univariate standard normal distribution and N=4. Suppose the sample is {-1, -1, 1, 1}. Then the joint probability density equals N(1 | mean=0, var=1) ^ 4. The probability density for the sample mean (-1 + -1 + 1 + 1) / 4 = 0 is N(0 | mean=0, var=0.25). Grab a calculator https://www.danielsoper.com/statcalc/calculator.aspx?id=54, we have that N(1 | mean=0, var=1) ^ 4 is about 0.24 ^ 4 and N(0 | mean=0, var=0.25) is about 0.79. Obviously, they differ. Intuitively, the probability of a sample mean collects the probability of all possible samples having this sample mean value, and should be larger than the probability of any single such sample.

[Rajon010]

Same issue in section 4.6.4.2.

[Rajon010]

Also, that N should be an exponent rather than a numerator.

[Rajon010]

Missing period.

[murphyk]

Re 3.65. I meant to write proportional to, not equality. See https://github.com/probml/pml-book/issues/512

[murphyk]

All fixed, thanks.