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Review for Final Study Guide 1. How to check to see if a function f(x) is a valid p.m.f/p.d.f. 2. How to calculate the mean, variance and standard deviation of any discrete/continuous random variable. 3. The rules for expectation, mean, and variance. 4. How to use a moment-generating function to find a mean and variance or to identify a p.m.f./p.d.f 5. The characteristics (p.d.f./p.m.f, mean, variance, moment generating function) of 9 distributions (4 discrete, 5 continous) 6. Know how to find probabilities for the named discrete/continuous distributions we studied. 7. How to find the cumulative distribution function of a continuous random variable. 8. How to verify that a joint p.m.f. (p.d.f.) is valid. 9. How to check that X and Y are independent. 10. How to calculate the mean and variance of a random variable given the joint p.m.f. (p.d.f). 11. How to find probabilities using a joint p.m.f. (p.d.f.). 12. How to find marginal distributions given the joint p.m.f. (p.d.f.) 13. How to calculate the covariance and correlation between X and Y (If X and Y are independent, then Corr(X,Y) = Cov(X,Y) = 0. However Corr(X,Y)=0 does not imply X and Y are independent). 14. How to find a conditional p.m.f./p.d.f. and how to verify that one is valid. 15. How to find a conditional mean and conditional variance. 16. How to use Z in finding probability of a normal random variable for some interval. 17. How to find probability of a random variable associated with a normal random n variable (e.g, Z2~X2(1), Z i 1 2 i ~ 2 (n) ).