Probability

Question 1

What is a Normal Distribution

Answer 1

The normal distribution is the most important continuous probability distribution and has the following properties:

It is bell-shaped and symmetric.

Its measures of central tendency (mean and median) are identical.

Its associated random variable has an infinite range

Question 2

Probability density function of the normal distribution

Answer 2

Notation is X~(U,O^2)

The mean μ shifts the distribution left or right

The standard deviation σ widens or narrows the curve

 Parameters μ and σ determines the central location and the shape of the distribution.

Question 3

What is the name for the normal distribution table reports probabilities implied by N(0,1).

Answer 3

Standard normal distribution N(0,1)

Question 4

The Central Limit Theorem (CLT)

Answer 4

For a sufficiently large sample (n), regardless the distribution of Xi, the sample mean X1/n∑􏰘􏰙􏰀 X􏰘i is approximately normally distributed.

Question 5

central limit theorem E(X bar & Z =

Answer 5

E(X BAR)=μ,var(X)=σ2 /n, andstd(X)=σ/ n

Z=(􏰖X-μ)/(σ/ n)~N(0,1)

Question 6

T stat vis Standard Normal

Answer 6

t has “fatter tails”, i.e. higher probability of

extreme values, relative to normal dist.

Question 7

why is F table used

Answer 7

The F distribution is used to test whether two populations have the same variance if both are normally distributed.