Continous Prabability Distributions

Question 1

Continuous variable

Answer 1

A random variable that can take any value within hits range

Question 2

Discrete random variable

Answer 2

Can only take some valued within it’s range

Question 3

For discrete random variables we could build a …

Answer 3

Probability distribution

X. P(X)

0. 0.01
1. 0.5
2. 0.4
3. 0.07
4. 0.02

This will not work for continuous data as there an infinite number of outcomes

Question 4

For continuous data we use

Answer 4

Probability density function

X axis includes all possible values of x

A PDF curve is above the x axis

The area under the curve between any two values of x is the probability that x lies between those two values

Total area under the curve must equal 1

Question 5

The normal distribution

Answer 5

Bell shaped and symmetric PDF from minus infinity to plus infinity

U (mean) = middle of curve

Notation = x ~ N(U,Ō^2)

U= mean
Ō^2= variance

Question 6

Central limit theorem

Answer 6

The total or mean of a large number of independent random variables with the same probability distribution has a normal distribution

90 similar trading days -total cash sales
Daily return on an ordinary share- monthly return

Returns on stocks
Pt= price of stock at time t

Return on stock is

Ft=Pt-P(t-)1/P(t-1)

Question 7

Special case the standard normal distribution , Z

Answer 7

A special case where the mean Is 0 and the deviation is 1

Nearly all data lies between 3 standard deviations of the mean