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Probability Fact
9,163 posts
Probability Fact
@ProbFact
Joined November 2009
- Var(X + Y) = Var(X) + Var(Y) + 2 Cov(X, Y)
- No, there’s a 50-50 chance two people share SOME birthday, not a PARTICULAR birthday.
- E( E(X|Y) ) = E(X)
- Most people have an above average number of legs.
- Uncorrelated random variables are not necessarily independent.
- Male heights have a normal distribution centered at 5' 10" with a standard deviation of 3 inches. The probability of an 8 foot tall man is on the order of 1 in 1,000,000,000,000,000,000. And yet there are men taller than 8'. The record is 8' 11".
- Var(X) = Var( E(X|Y) ) + E( Var(X|Y) )
- Var(X + Y) = Var(X) + Var(Y) + 2 Cov(X, Y)
- Var(X + Y) = Var(X) + Var(Y) + 2 Cov(X, Y)
- "Probability is the intersection of the most rigorous mathematics and the messiest of life." -- Nassim Taleb
- Discrete probability is conceptually easier than continuous probability because counting is easier than measure theory.
- A random variable is a measurable function on a probability space.
