Chapter 3 Flashcards
What to do in joint continuous distribution?
Do a 3D graph to see which square do you have to calculate.
If Cov(x,y) = 0 are x and y necessarily independent?
No
If E(x ⋅ y) = E(x) ⋅ E(y) are x and y necessarily independent?
No
Cov(x,y) = ?
E(x⋅ y) - E(x) ⋅ E(y)
𝜌_x,y = Corr[X, Y] = ?
Cov(x,y)/(SD(x) ⋅ SD(y))
Multinomial distribution
n!/x_i! ⋅ P(x_i)
E(s) = ?
n ⋅ E(x_i)
VAR(s) = ?
n ⋅ VAR(x_i)
E(x̄) = ?
E(x_i)
VAR(x̄) = ?
VAR(x_i)/n
VAR(x) = ? using the law of total variance
E(VAR(X|Y)) + VAR(E(X|Y))
Continuous correction?
If x > 3 —> x > 3.5
If x< 3 —> x < 2.5
Order statistic min
(S_x(x))^n
Order statistic max
(F_x(x))^n
Shortcut for continuous uniform
E(x_min) = a + (b-a)/n+1
E(x_max) = b - (b-a)/n+1