Probability and Distributions God-Sheet Deck Flashcards
P(A|B)=?
P(AnB)/P(B)
P(AnB)=?
P(A|B)P(B)=P(B|A)P(A)
if independent, what is P(AnB)?
P(A)*P(B)
E(aX+b)=?
aE(X)+b
Var(aX+b)=?
a^2Var(X)
What is the interpolation formula?
%(z)=%(a)+((z-a)/(b-a))*(%(b)-%(a))
What is the cdf of the Gamma Distribution?
cdf=1-(sum of, from k=0, a-1) (1/k!)*(x/B)^ke^(-x/B)
What is the formula for P(X=xi,Y=yi)?
(sum of, i)(sum of, j) P(X=xi,Y=yi)
Expected value for X for two random variables?
E(X)=(sum of, i)xiP(X=xi)
P(Y=y|X=x)=?
P(X=x,Y=y)/P(X=x)
Cov(X,Y)=?
Cov(X,Y)=E(XY)-E(X)E(Y)
E(XY)=?
E(XY)=(sum of, i)(sum of, j) xiyiP(X=xi, Y=yi)
What is the definition of Covariance?
Covariance is a measure of how X and Y vary together
What is the formula for correlation?
Correlation: p(X,Y)=Cov(X,Y)/(Var(X)Var(Y))^(1/2)
What is the pdf when you have 2 variables which are continuous?
pdf= (integral, -inf, +inf)(integral, -inf, +inf) f(x,y) dxdy = 1
What is the pdf when you have 2 variables?
pdf= (integral, -inf, +inf) f(x,y) dx * (integral, -inf, +inf) f(x,y) dy) =marginal pdf of y*marginal pdf of x
When summing discrete random variables, E(Y)=?
E(Y)=E(X1)+E(X2)+…+E(Xn)
When summing discrete random variables, Var(Y)=?
Var(Y)=Var(X1)+Var(X2)+…+Var(Xn) +n*Cov(X1,X2,…,Xn)
When summing ‘r’ geometric random variables, E(Y)=?
E(Y)=r/p
When summing ‘r’ geometric random variables, Var(Y)=?
Var(Y)=r(1-p)/p^2
When summing ‘n’ Poisson variables, E(Y)=?
E(Y)=Var(Y)=(sum of, i=1, n) (lambda i)
Briefly describe the Central Limit Theorem
The Central Limit Theorem states that, given sufficient trials, the true mean will be found
What is the formula for the Central Limit Theorem
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
What is the formula for a Poisson approximation by a standard normal?
W=((sum of, i=1, lambda) Yi - (lambda))/(lambda)^(1/2)
How is a binomial approximated by a normal?
Bi ~ N(np, np(1-p))
