{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture 2

# Lecture 2 - Probability distribution Outcomes mutually...

This preview shows pages 1–4. Sign up to view the full content.

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

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

View Full Document
Normal distribution: The probability distribution function of a normal random variable X is: µ= location parameter , σ²= scale parameter (lower sigma indicates more ‘spread out’) We usually denote a normal random variable as X N(μ,σ²). When μ=0 and σ²=1, we have a standard normal distribution. We usually denote a standard normal random variable as z, with the cumulative distribution function being: P(Z≤z)=Φ(z) If X N(μ,σ²), then Y=(X-μ)/σ 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 ) = μ Y = long-run average value of Y over repeated realizations of Y variance = E ( Y μ Y )P 2 = 2 Y σ = measure of the squared spread of the Distribution standard deviation = variance = σ Y Example:
Example: Example: If Y N(μ,σ²), then the mean of Y is μ, the variance of Y is σ². 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+… = -.105

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}