8

Question 1

X is a standard normal random variable if: f(x) = ?

Answer 1

(1/(2 pi)^1/2) e^(-x^2 / 2)

Question 2

Expectation of a standard normal random variable: E[X] = ?

Answer 2

Int(-oo -> oo)(x f(x) dx) = 0

Question 3

Every odd function integral from -oo to oo = ?

Answer 3

0

Question 4

Variance of standard normal random variable: var[X] = ?

Answer 4

Int(f(x) x^2 dx) = int(-oo -> oo)((1/(2 pi)^1/2) e^(-x^2 /2) x^2 dx) = 1

Question 5

Expression for general normal random variable: f_y (x) = ?

Answer 5

(1/((2 pi)^1/2 sigma) e^(-(x - mu)^2 / 2 sigma^2)

Question 6

Expectation of normal random variable: E[X] = ?

Answer 6

Mu

Question 7

Variance of normal random variable: var[X] = ?

Answer 7

Sigma^2

Question 8

Cumulative distribution function of normal variable: F_x (a) = ?

Answer 8

Phi(a) = (1/(2 pi)^-1/2) int(-oo -> a)(e^-(x^2 / 2) dx)

Question 9

What is special about a normal random variable?

Answer 9

They approximate the binomial distribution for a large n.

Question 10

the cumulative density function of the standard density function is?

Answer 10

phi

Question 11

Standard error: What happens if you divide the error by the size of the standard deviation?

Answer 11

Number of standard deviations from the mean

Question 12

Error from the mean?

Answer 12

S_n - np

Question 13

DeMoivre-Laplace Limit Theorem: the equation, standard error for Bernoulli trial: lim(n->oo)(P{a <= (S_n - np)/(npq)^1/2) <= b}) = ?

Answer 13

phi(b) - phi(a)