Chapter 7: Continuous Distribution Spring 2016

Random Variable Random Variable Characteristics Example Discrete Random Variable Finite number of outcomes Binomial Distribution Continuous Random Variable Unlimited number of possible outcomes Uniform Distribution; Normal, Standard normal, Student’s t distribution ---What about P(x=X) in each case?

Continuous Distribution Parameters Mean Spread Condition Normal N(µ , σ ) µ σ Use when σ is known Standard Normal N(0, 1) 1 Use when σ is known, after standardization 𝑧= 𝑥−𝜇 𝜎 Student’s t t(df) df Use when σ is unknown but s is known; standardizing by 𝑡= 𝑥−𝜇 𝑠

Finding Probabilities Distribution Probability P(x<X) Normal Area under curve NORM.DIST(X, µ , σ ,1) Standard Normal NORM.S.DIST(Z,1) Student’s t T.DIST(T,df,1)

Finding Probabilities How about P(X>b)? P(X>b)=1-P(X<b) And P(a<X<b)? P(a<X<b)=P(X<b)-P(X<a)

Finding values given probabilities Distribution Value at which P(x<X)=π From standardized scores Normal X = NORM.INV(π, µ , σ) NA Standard Normal Z = NORM.S.INV(π) 𝑋=𝑍∗𝜎+𝜇 Student’s t 𝑇 = T.INV(π,df) 𝑋=𝑇∗𝑠+𝜇