General Flashcards
What is the expansion for e^x?
e^x = 1 + x + x^2/2! + x^3/3! + ….
What is the mean and variance of the Binomial Distribution?
X~Bin(n,p)
n number of trials
p probability of success of each trial
Mean = np
Variance = np(1-p)
What is the variance formula with 2 variable with the correlation coefficient?
Var(ax+by) a^2var(x) +b^2var(y) +2absd(x)sd(y)* p
where p is the correlation coefficient
What is the formula for the mean of a discrete distribution?
E[X] = sum[x*P(x=x)]
What is the formula for the mean of a continuous distribution?
E[x] = int[a,b] x*f(x) dx
What is the formula for the variance of a discrete distribution?
sum[(mu-x)^2 * P(X=x)]
Alternatively we have,
Var[x] = E[x^2] - E[x]^2
What is the mean and variance of a uniform distribution?
Mean = (b-a)/2
Variance = (b-a)^2/12
What is the pdf of a uniform distributions i.e. f(x)?
1/(b-a)
What is the pdf of the exponential distribution?
If X~exp(lambda) then lambda = 1/mu
f(x) = lambdaexp(-lamdax) for x>=0
f(x) =0 for x<0
What is the formula for P(X<x) and P(X>x) if X~exp(lambda)?
P(X>x) = exp(-lambdax)
P(X<x) = 1-exp(-lambdax)
given that x>0
How do you find the gradient of a line when you have points that sit on the line itself?
“Up over across”
(y2-y1)/(x2-x1)
What it the Covariance formula?
Cov(x,y) = psigma_xsigma_y
What are the covariance identities?
Cov(ax+b,cy+d) =cov(ax,cy) + cov(ax,d) + cov(b,cy) + cov(d,b)
Cov(ax+b,cy+d) =accov(x,y) + 0 + 0 + 0
Cov(x,x) = var(x)
What is the binominal distribution probability function? (Px=x)
P(X=x) = nCx * p^x * (1-p)^(n-x)
n - number of trials
p - probability of success
What is the nCx formula?
n!/x!*(n-x)!
