Continuous Random Variables

Question 1

Bell shaped symmetric curve centered at μ and whose shaped is determined by σ^2

Answer 1

Normal Gaussian
x ~ normal ( μ , σ^2 )

Question 2

for normal distribution z =

Answer 2

z = ( x - μ ) / σ

Question 3

monitor continuously
RV is T: the waiting time between the next event (between any two events)

Answer 3

exponential (a continuous) RV
T ~ exponential (λ)
T: the waiting time between the next event (between any two events)
To find the probability p(T</>t) integrate from 0 to t the term λe^-(λt)

Question 4

sample mean (x-bar)

Answer 4

regular average
(x1+x2+…xn) / n

Question 5

μ for approximately normal RV

Answer 5

refer to binomial μ
μ = n*p

Question 6

σ^2 for approximately normal RV

Answer 6

refer to binomialσ^2
σ^2 = np(1-p)

Question 7

For many trials of independent identically distributed random variable with E(x) = μ and variance σ^2, the distribution of the sum approaches normal distribution

Answer 7

Central Limit Theorem:
For many trials of independent identically distributed random variable with E(x) = μ and variance σ^2, the binomial distribution approaches normal distribution

Question 8

What is a sample sum?

Answer 8

Sample Sum = S-bar = X1 + X2 + X3…Xn
so that E(Sn) = E(X1) + E(X2) + … E(Xn) = n * μ
and Var(Sn) = var(X1) + var(X2) + … var(Xn) = n * σ^2

Question 9

sample sum normal distribution

Answer 9

Sn ~ N( nμ , n σ^2 )
E(Sn) = nμ
var(Sn) = n σ^2

Question 10

sample mean normal distribution

Answer 10

X-bar ~ N( μ , σ^2 / n )
E(x-bar) = μ
var(x-bar) = σ^2 / n

Question 11

probability statement for normal distribution

Answer 11

p(x-bar </> #)
# = x-bar in the z forumla

Question 13

A statistic that is used to estimate an unknown constant or parameter

Answer 13

point estimator or point estimate (p-hat)

Question 14

Most often used to evaluate the overall goodness of an estimator

Answer 14

Mean square error = E( ( p-hat - pop.parameter )^2 )