Stats

Question 1

Confidence intervals equation

Answer 1

mean in interval [ (sample mean) - (z * s.d.)/root n , (sample mean) + (z * s.d.)/root n ]

Find z by doing inverse normal of z graph, area = confidence interval, tail = central

Question 2

Poisson distribution equation + meaning

Answer 2

Expectation = variance = lambda

P(X=r) = (e^(-lambda) * lambda^(r))/r!

E(aX + bY) = aE(X) + bE(Y)
Var(aX + bY) = a^2 Var(X) + b^2 Var (Y)

Question 3

Geometric Distribution equations + meaning

Answer 3

Repeat until first ‘success’
Probability of success = p

X~geo(p)
P(X=1) = p
P(X=2) = (1-p)*p
P(X=3) = (1-p)^2 *p
P(X=r) = (1-p)^(r-1) * p

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

Question 4

Exponential function

Answer 4

f(x) = lambda * e^(-lambda * x)
E(X) = 1/lambda
Var(X) = 1/lambda^2

Question 5

Sequences and series

sum up to n of 1, r=1

Answer 5

= n

Question 6

Sequences and series

sum up to n of r, r=1

Answer 6

= n/2 (n+1)

Question 7

Sequences and series

sum up to n of r^2, r=1

Answer 7

= n/6 (n+1)(2n+1)

Question 8

Sequences and series

sum up to n of r^3, r=1

Answer 8

= (n^2)/4 (n+1)^2