2 - discrete random variables

Question 1

expectation (E(X))

Answer 1

sum of xi pi

Question 2

variation (X)

Answer 2

E(x^2) - (E(x))^2
sum of xi^2 pi - (sum of xi pi)^2

Question 3

linear coding

Answer 3

if Y = aX+ b
E(Y) = aE(X) + b
Var(Y) = a^2Var(X)
sd(Y) = a(sd(X))

Question 4

discrete uniform distribution
P(X = x)

Answer 4

X ∼U(n)
P(X = x) = 1/n

Question 5

discrete uniform distribution

Answer 5

a fixed no. n = spaced numerical outcomes with constant and = prob of them occurring

Question 6

if X ∼ U (n) the E(X) and the Var(X) are…

Answer 6

E(X) = n+1 /2
var(X) n^2 -1 /12

Question 7

binomial distribution E(X) and Var(X)…

Answer 7

if X ∼ B(n, p)
E(X) = np
Var(X) == np(1-p)

Question 8

geometric distribution conditions

Answer 8

• there are trials where all outcomes can be success of failure
• independent trials
• p is constant
• no upper limit to the no. trials

Question 9

geometric distribution P(X = x)

Answer 9

if X ∼ Geo(p)
P(X = x) = p(1-p) ^x-1

Question 10

geometric distribution P(X > x)

Answer 10

(1-p) ^x

Question 11

geometric distribution E(X) and Var(X)…

Answer 11

if X ∼ Geo(p)
E(X) = 1/p
Var(X) = (1-p) /p^2