This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Probability distribution Outcomes: mutually exclusive and collectively exhaustive Probability: relative frequency Cumulative probability distribution The probability that a random variable Y is less than or equal to a particular value y; Y for random variable and y for a number. Example: computer crashes when writing a term paper Bernoulli random variable: Regression with binary dependent variables Example: mortgage loan applications; credit card applications; default risk Continuous random variable Cumulative probability distribution Probability distribution Normal distribution: The probability distribution function of a normal random variable X is: = location parameter , = scale parameter (lower sigma indicates more spread out) We usually denote a normal random variable as X N(,). When =0 and =1, we have a standard normal distribution. We usually denote a standard normal random variable as z, with the cumulative distribution function being: P(Zz)=(z) If X N(,), then Y=(X)/ is a standard normal . variable : Example X N(2,4), what is P(X<1.8)? P(X>2)? P(1.5<X<3)? mean = expected value (expectation) of Y = E ( Y ) = Y = longrun average value of Y over repeated realizations of Y variance = E ( Y Y )P 2 = 2 Y = measure of the squared spread of the Distribution standard deviation = variance = Y Example: Example: Example: If Y N(,), then the mean of Y is , the variance of Y is . Useful formulas: Random variables X and Z have a joint distribution Pr(X=x, Z=z) Marginal distribution E(M) = 0*.8+1*.1+2*.06+3*.03+4*.01=.36 E(A) = 1*.5+0*.5=.5 cov(M,A) = (0.36)(0.5)*.35 + (1.36)(1.5)*.065+ = .105cov(M,A) = (0....
View
Full
Document
This note was uploaded on 11/23/2009 for the course FIN 5290 taught by Professor Li during the Fall '09 term at Temple.
 Fall '09
 Li

Click to edit the document details