TDSM 2.1

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Let A is the event that people like butter RightarrowP(A)=0.8


Probability


2-1. Suppose 80% of people like peanut butter, 89% like jelly, and 78% like both. Given that a randomly sampled person likes peanut butter, what is the probability that she also likes jelly?

(Solution 2.1)


2-3. Consider a game where your score is the maximum value from two dice. Compute the probability of each event from {1,,6}

(Solution 2.3)


2-5. If two binary random variables X and Y are independent, is ˉX (the complement of X) and Y also independent? Give a proof or a counterexample.

(Solution 2.5)


Statistics


2-7. Construct a probability distribution where none of the mass lies within one σ of the mean.

(Solution 2.7)


2-9. Show that the arithmetic mean equals the geometric mean when all terms are the same.

(Solution 2.9)


Correlation Analysis


2-11. What would be the correlation coefficient between the annual salaries of college and high school graduates at a given company, if for each possible job title the college graduates always made:

  1. 5,000 dollars more than high school grads?
  2. 25% more than high school grads?
  3. 15% less than high school grads?

(Solution 2.11)


2-13. Use data or literature found in a Google search to estimate/measure the strength of the correlation between:

  1. Hits and walks scored for hitters in baseball.
  2. Hits and walks allowed by pitchers in baseball.

(Solution 2.13)


Logarithms


2-15. Show that the logarithm of any number less than 1 is negative.

(Solution 2.15)


2-17. Prove that xy=b(logbx+logby)