5

Question 1

Mean = ?

Answer 1

E[X]

Question 2

Variance? (2•)

Answer 2

•E[X^2] or •E[(mu - X)^2]

Question 3

Binomial formula (a + b)^n?

Answer 3

Sum(k=1 -> n)((n chose k) a^k b^(n - k))

Question 4

If p = 1/2, then what is binomial variable?

Answer 4

(n chose k) 1/2^n

Question 5

What does p mean in binomial variable?

Answer 5

The probability that we are looking for in the question.

Question 6

Identity: i(n chose i) = ?

Answer 6

n(n-1 chose i-1)

Question 7

E(X) of binomial random variable B(b,p) is?

Answer 7

Sum(i=0 -> n)(i(n chose i)p^i q^n-i)

Question 8

Mean of binomial random variable?

Answer 8

np

Question 9

If X represents the number of heads in n tosses (wth probability of p), then E(X_j) =?

Answer 9

p1 + (1-p)0

Question 10

E[(Y + 1)^(k-1)] = ?

Answer 10

Sum(i=0 -> n-1)((n-1 chose i)p^i q^((n-1)-i)*(j+1)^(k-1))

Question 11

Probability mass function for binomial random variable with parameters (n,p)?

Answer 11

(n chose k)p^k q^(n-k)

Question 12

E[X^k] = ?

Answer 12

npE[(Y + 1)^(k-1)], Y is binomial random variable with parameters (n-1, p).

Question 13

Var[X] with binomial random variable B(n, p)?

Answer 13

npq

Question 14

e^x = ?

Answer 14

Lim(n->oo)(1 + x/n)^n

Question 15

Poisson Distribution: (Lambda^k/k!)(1-p)^n-k ~ ?

Answer 15

(Lambda^k /k!) e^-lambda

Question 16

Poisson Random variable X?

Answer 16

Parameter (lambda) that satisfies the Poisson distribution for an integer k>= 0

Question 17

Taylor expansion of e^lambda = ?

Answer 17

Sum(k=0 -> oo)(lambda^k/k!)

Question 18

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

Answer 18

Lambda

Question 19

Variance of Poisson distribution: Var[X] = ?

Answer 19

Lambda

Question 20

When Poisson distribution should be used? All must be true •5

Answer 20

•n (trials) is very big
•p is very small
•np = lambda, is reasonable
•Independent trials
•Fixed p (doesn’t depend on anything)