Daily Dozen:
1. What's the difference between the statistical "mean" and the colloquial "average," or, as commonly understood, the most likely value? What is actually the most likely value?
2. Show that, if two events are independent, p(A)p(B) = p(A,B).
3. What distribution could be used to model the probability of finding two or more cancer cells in a healthy lung biopsy?
4. What distribution could be used to model the distances between two instances of a genetic element (binding site, for example) in DNA?
5. Write out the probability that, given events A, B, and C that are independent, none of them occur.
6. Draw a histogram for which the mean, median and mode are all different.
7. What's the difference between a combination and a permutation?
8. Show that nCk is the same as nC(n-k).
9. What's the significance of 2 standard deviations, when talking about the normal distribution?
10. For three events A, B, and C, where p(A,B, and C) > 0, why does p(A or B or C) != p(A) + p(B) + p(C)? What is the correct calculation?
11. Write an algorithm describing how to wash a car.
1. What's the difference between the statistical "mean" and the colloquial "average," or, as commonly understood, the most likely value? What is actually the most likely value?
2. Show that, if two events are independent, p(A)p(B) = p(A,B).
3. What distribution could be used to model the probability of finding two or more cancer cells in a healthy lung biopsy?
4. What distribution could be used to model the distances between two instances of a genetic element (binding site, for example) in DNA?
5. Write out the probability that, given events A, B, and C that are independent, none of them occur.
6. Draw a histogram for which the mean, median and mode are all different.
7. What's the difference between a combination and a permutation?
8. Show that nCk is the same as nC(n-k).
9. What's the significance of 2 standard deviations, when talking about the normal distribution?
10. For three events A, B, and C, where p(A,B, and C) > 0, why does p(A or B or C) != p(A) + p(B) + p(C)? What is the correct calculation?
11. Write an algorithm describing how to wash a car.