S2- Continuous Distributions

Question 1

What is the continuous uniform distribution?

Answer 1

A continuous random variable that has a uniform distribution over the interval (a,b)

Question 2

What is the pdf of a continuous uniform distribution?

Answer 2

f(x) = 1/(b-a) a

Question 3

What is the E(x) of a continuous uniform distribution?

Answer 3

(a+b)/2

Question 4

What is the variance of a continuous uniform distribution?

Answer 4

(1/12)(b-a)^2

Question 5

When must the continuity correction be applied?

Answer 5

When going from a discrete variable to a continuous variable

Question 6

What is the binomial approximation to the normal? (X~B(n,p))

Answer 6

Y~N(np,npq)

Question 7

What are the conditions required to approximate the binomial to the normal?

Answer 7

n is large and p is close to 0.5

np and nq are both >5

Question 8

What is the Poisson approximation to the normal? (X~Po(𝜆))

Answer 8

Y~N(𝜆,𝜆)

Question 9

What is the condition required to approximate the Poisson to the normal?

Answer 9

𝜆>10

Question 10

How do you get from X~N(μ,σ^2) to values you can look up in the normal distribution table?

Answer 10

(X-μ)/σ