Continuous Random Variables Flashcards

1
Q

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

A

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

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2
Q

for normal distribution z =

A

z = ( x - μ ) / σ

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3
Q

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

A

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)

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4
Q

sample mean (x-bar)

A

regular average
(x1+x2+…xn) / n

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5
Q

μ for approximately normal RV

A

refer to binomial μ
μ = n*p

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6
Q

σ^2 for approximately normal RV

A

refer to binomialσ^2
σ^2 = np(1-p)

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7
Q

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

A

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

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8
Q

What is a sample sum?

A

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

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9
Q

sample sum normal distribution

A

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

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10
Q

sample mean normal distribution

A

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

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11
Q

probability statement for normal distribution

A

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

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12
Q
A
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13
Q

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

A

point estimator or point estimate (p-hat)

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14
Q

Most often used to evaluate the overall goodness of an estimator

A

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

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