Answer by Stephan Kolassa for Why is E(θ / (1 - θ)) different than E(θ) / (1...
Taking an expectation does not commute with all arithmetic operations. While $E(X+Y)=EX+EY$, such a "distributivity" does not hold for other operations. For instance, the expectation of a product of...
View ArticleWhy is E(θ / (1 - θ)) different than E(θ) / (1 - E(θ))?
I've encountered a problem question:The probability of success for a random variable follows a Beta(5, 3) distribution.The posterior mean is θ = 0.625.The odds of success is defined as θ / (1 -...
View ArticleAnswer by Mateen Ulhaq for Why is E(θ / (1 - θ)) different than E(θ) / (1 -...
Let's consider a uniformly distributed random variable: $\theta \sim U(-\frac{1}{2}, \frac{1}{2})$. Then evidently,$$E[\theta]= \int_{-\infty}^{\infty} \theta \, p(\theta) \, d\theta=...
View Article
More Pages to Explore .....
