1. UNR, MATH/STAT 352, Spring 2007

2. Binomial(n,p) UNR, MATH/STAT 352, Spring 2007

3. Binomial(1,0.5) Number of successes within 1 symmetric Bernoulli trial can only be 0 or 1. These possibilities have equal chances. UNR, MATH/STAT 352, Spring 2007

4. Binomial(2,0.5) Number of successes within 2 symmetric Bernoulli trials can only be 0, 1 or 2. The possibility to have exactly 1 success is larger than that of having 0 or 2. A fair game should result in a tie. Then why do people play fair games? UNR, MATH/STAT 352, Spring 2007

5. Binomial(2,0.1) Most likely there will be no successes UNR, MATH/STAT 352, Spring 2007

6. Binomial(2,0.9) Most likely there will be only successes UNR, MATH/STAT 352, Spring 2007

7. Binomial(15,0.1) Unimodal (mode = 1) Right-skewed Concentrated around 1.5 (E = np = 1.5) UNR, MATH/STAT 352, Spring 2007

8. Binomial(19,0.1) Unimodal (mode = 1-2) Right-skewed Concentrated around 1.5 UNR, MATH/STAT 352, Spring 2007

9. Binomial(100,0.1) Unimodal (mode = 10) Symmetric? (E = np = 10) Concentrated around 10 P(10+3) < P(10-3) UNR, MATH/STAT 352, Spring 2007

10. Binomial(100,0.9) Unimodal (mode = 90) Symmetric? (E = np = 90) Concentrated around 90 UNR, MATH/STAT 352, Spring 2007

11. Bin(100,0.9)Bin(100,0.1) Only a small fraction of possible outcomes has not negligible P (i.e. only small part can be seen in experiment) P is very small (not 0!) here UNR, MATH/STAT 352, Spring 2007

12. Binomial(6,0.5) Here all possible outcomes have reasonable probabilities UNR, MATH/STAT 352, Spring 2007

13. Poisson( ) UNR, MATH/STAT 352, Spring 2007

14. Poisson(1) Binomial(1000,.001] I’ve seen this already! UNR, MATH/STAT 352, Spring 2007

15. ++ Binomial(n,p)  Poisson( ) UNR, MATH/STAT 352, Spring 2007

16. Poisson Binomial Normal Poisson(30)Binomial(1000,.03)N(30,sqrt(30)) UNR, MATH/STAT 352, Spring 2007

17. If n is large ( n > 100), p is small ( p < 0.05), and both np and n (1- p ) are not small (say >10) then B(n,p)~P(np)~N(np, np(1-p)) UNR, MATH/STAT 352, Spring 2007