Probability and Distributions God-Sheet Deck

Question 1

P(A|B)=?

Answer 1

P(AnB)/P(B)

Question 2

P(AnB)=?

Answer 2

P(A|B)P(B)=P(B|A)P(A)

Question 3

if independent, what is P(AnB)?

Answer 3

P(A)*P(B)

Question 4

E(aX+b)=?

Answer 4

aE(X)+b

Question 5

Var(aX+b)=?

Answer 5

a^2Var(X)

Question 6

What is the interpolation formula?

Answer 6

%(z)=%(a)+((z-a)/(b-a))*(%(b)-%(a))

Question 7

What is the cdf of the Gamma Distribution?

Answer 7

cdf=1-(sum of, from k=0, a-1) (1/k!)*(x/B)^ke^(-x/B)

Question 8

What is the formula for P(X=xi,Y=yi)?

Answer 8

(sum of, i)(sum of, j) P(X=xi,Y=yi)

Question 9

Expected value for X for two random variables?

Answer 9

E(X)=(sum of, i)xiP(X=xi)

Question 10

P(Y=y|X=x)=?

Answer 10

P(X=x,Y=y)/P(X=x)

Question 11

Cov(X,Y)=?

Answer 11

Cov(X,Y)=E(XY)-E(X)E(Y)

Question 12

E(XY)=?

Answer 12

E(XY)=(sum of, i)(sum of, j) xiyiP(X=xi, Y=yi)

Question 13

What is the definition of Covariance?

Answer 13

Covariance is a measure of how X and Y vary together

Question 14

What is the formula for correlation?

Answer 14

Correlation: p(X,Y)=Cov(X,Y)/(Var(X)Var(Y))^(1/2)

Question 15

What is the pdf when you have 2 variables which are continuous?

Answer 15

pdf= (integral, -inf, +inf)(integral, -inf, +inf) f(x,y) dxdy = 1

Question 16

What is the pdf when you have 2 variables?

Answer 16

pdf= (integral, -inf, +inf) f(x,y) dx * (integral, -inf, +inf) f(x,y) dy) =marginal pdf of y*marginal pdf of x

Question 17

When summing discrete random variables, E(Y)=?

Answer 17

E(Y)=E(X1)+E(X2)+…+E(Xn)

Question 18

When summing discrete random variables, Var(Y)=?

Answer 18

Var(Y)=Var(X1)+Var(X2)+…+Var(Xn) +n*Cov(X1,X2,…,Xn)

Question 19

When summing ‘r’ geometric random variables, E(Y)=?

Answer 19

E(Y)=r/p

Question 20

When summing ‘r’ geometric random variables, Var(Y)=?

Answer 20

Var(Y)=r(1-p)/p^2

Question 21

When summing ‘n’ Poisson variables, E(Y)=?

Answer 21

E(Y)=Var(Y)=(sum of, i=1, n) (lambda i)

Question 22

Briefly describe the Central Limit Theorem

Answer 22

The Central Limit Theorem states that, given sufficient trials, the true mean will be found

Question 23

What is the formula for the Central Limit Theorem

Answer 23

W=((sum of, i=1, n)Xi - (true mean)n)/((standard deviation)(n)^(1/2)) which will roughly approximate to a standard normal distribution as n –> infinity

Question 24

What is the formula for a Poisson approximation by a standard normal?

Answer 24

W=((sum of, i=1, lambda) Yi - (lambda))/(lambda)^(1/2)

Question 25

How is a binomial approximated by a normal?

Answer 25

Bi ~ N(np, np(1-p))