1.1.Probability of a Region R Assuming n samplesx1,x2,...,x,sampled from the probability density distribution p(x),then the probability P ofa vectorx in a region R is: P-p)dx. Then,for n samples,the probability of k samples in region R is determined by binomial distribution. P=()P-P From expectation and variance of the random variable k: Ek=nP Var(k)=nP(1-P) It is not easy to calculate Ek]=okPx and Var]=(k-Ek])2P directly 6/451.1. Probability of a Region R ▶ Assuming n samples x1, x2, ..., xn, sampled from the probability density distribution p(x), then the probability P of a vector x in a region R is: P = Z R p(x ′ )dx′ . ▶ Then, for n samples, the probability of k samples in region R is determined by binomial distribution. Pk =  n k  P k (1 − P) n−k . ▶ From expectation and variance of the random variable k: E[k] = nP Var(k) = nP(1 − P) ▶ It is not easy to calculate E[k] = Pn k=0 kPk and Var[k] = Pn k=0(k − E[k])2Pk directly 6 / 45