The Normal Distribution

Question 1

E(X1 + X2) =

Answer 1

E(X1) + E(X2)

Question 2

E(X1 - X2) =

Answer 2

E(X1) - E(X2)

Question 3

Var(X1 + X2) =

Answer 3

Var(X1) + Var(X2)

Question 4

Var(X1 - X2) =

Answer 4

Var(X1) + Var(X2)

Question 5

what does “o/” signify

Answer 5

probability density function (pdf)

Question 6

what does u and o^2 signify

Answer 6

• u = mean

- o^2 = variance where o = standard deviation

Question 7

if X~N(u , o^2), o/(x) =

Answer 7

(1 / o * root of 2pi) * e^(-1/2(x - u / o)^2)

Question 8

what is the equation for z in the standardised form

Answer 8

z = x - u / o

Question 9

what is the standardized normal distribution

Answer 9

Z~N(0,1)

Question 10

what is the pdf for the standardised normal distribution

Answer 10

(1 / root of 2pi) * e^(-z^2 / 2)

Question 11

what does the symbol “oT” singnify

Answer 11

the cumilative distribution function (cdf)

Question 12

what does P(Z < z) =

Answer 12

oT(z)

Question 13

what does oT(z) =

Answer 13

(1 / root of 2pi) * integration of e^(-1/2 *u^2) with limits z and -infinity

Question 14

If X1~N(u1 , a^2) and X2~N(u2, b^2), (X1 + X2)~ what

Answer 14

N(u1 + u2 , a^2 + b^2) only true for independent random variables

Question 15

If X~N(u, o^2), what does aX + b equal

Answer 15

aX + b~N(au +b, a^2 * o^2)