Unformatted text preview: Rob Bayer Math 55 Worksheet July 31, 2009 Independence of R.V.’s, Chebyshev’s Inequality 1. Determine whether each of the following pairs of random variables are independent or not: (a) X=“number of heads,” Y=“number of tails,” when three fair coins are flipped (b) X=“sum of dice,” Y=“value of first die” when two fair dice are tossed (c) X =“sum of dice mod 2”, Y=“value of first die” when two fair dice are tossed 2. Suppose two professors are co-teaching a course and trying to write a midterm. If they have a bank of k 2 problems to choose from and each (independently) chooses k problems they want to put on the exam, what is the expected number of problems chosen by both professors? Hint: make a r.v.’s X i ,Y i for whether each professor chose problem i or not. 3. Consider the experiment in which you flip a fair coin 3 times. Determine V ( X ) and σ ( X ) for each of the following: (a) X =“number of heads” (b) X =“longest consecutive run of the same result”...
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This note was uploaded on 09/10/2009 for the course MATH 55 taught by Professor Strain during the Summer '08 term at Berkeley.
- Summer '08