{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Session2 - Review of Probability and Statistics Dr Salman...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Review of Probability and Statistics Dr. Salman Khan PhD. Finance
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
2 Random Variables X is a random variable if it represents a random draw from some population a discrete random variable can take on only selected values a continuous random variable can take on any value in a real interval associated with each random variable is a probability distribution
Background image of page 2
3 Random Variables Examples the outcome of a coin toss a discrete random variable with P(Heads)=.5 and P(Tails)=.5 the height of a selected student a continuous random variable drawn from an approximately normal distribution
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
4 Expected Value of X E(X) The expected value is really just a probability weighted average of X E(X) is the mean of the distribution of X, denoted by m x Let f(x i ) be the probability that X=x i , then n i i i X x f x X E 1 ) ( ) ( m
Background image of page 4
5 Variance of X Var(X) The variance of X is a measure of the dispersion of the distribution Var(X) is the expected value of the squared deviations from the mean, so 2 2 ) ( X X X E X Var m
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
6 More on Variance The square root of Var(X) is the standard deviation of X Var(X) can alternatively be written in terms of a weighted sum of squared deviations, because i X i X x f x X E 2 2 m m
Background image of page 6
7 Covariance Cov(X,Y) Covariance between X and Y is a measure of the association between two random variables, X & Y If positive, then both move up or down together If negative, then if X is high, Y is low, vice versa Y X XY Y X E Y X Cov m m ) , (
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
8
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}