Extra Equations

Question 1

Mean Coefficient Update Rule

Answer 1

(mu)j_new = 1/(N_1) [sum n=1 to N]{zeta(Znj)*(xn)}

Question 2

Mixture Coefficient Update Rule

Answer 2

(Pi)j_new = Nj/N

Question 3

Give the formulae for the maximum likelihood estimates of the distribution’s mean (mu) and
covariance matrix (sigma).

Answer 3

(mu)[cap] = 1/N [sum i=1 to N]{xi} = x[bar]

(Sigma)[cap] = 1/N [sum i=1 to N] {(xi - (mu)[cap])(xi - (mu)[cap])^T}

Question 4

x1,x2,x3 univariate gaussian unknown mean variance = 1
Give a single expression for joint density and the likelihood of the mean

Answer 4

N(x1,x2,x3|mu, sigma^2=1) = (1/(2pi)^(1/2))^3 exp [-1/2 sum(i=1 to 3) {(xi-mu)^2}]