Probability and Computing: Chapter 3 Exercises

Exercise 3.2: Let X be a number chosen uniformly at random from [-k,k]. Find Var[X].

Exercise 3.7: A simple model of the stock market suggests that, each day, a stock with price q will increase by a factor r>1 to qr with probability p and will fail to \frac{q}{r} with probability 1-p. Assuming we start with a stock with price 1, find a formula for the expected value and the variance of the price of the stock after d days.

Exercise 3.10: For a geometric random variable X, find E[X^{2}] and E[X^{4}]. (Hint: Use the lemma 2.5)

Exercise 3.12: Find an example of a random variable with finite expectation and unbound variance.Give a clear argument showing that your choice has these properties.

Exercise 3.13: Find an example of a random variable with finite jth moments for 1 \leq j \leq k but an unbound (k+1)th moment. Give a clear argument showing that your choice has these properties.

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3 responses to this post.

  1. fuck, you have no answers!

    Reply

  2. Posted by Anonymous on December 24, 2013 at 11:52 pm

    Where is the solution ???

    Reply

  3. Posted by anik on March 2, 2017 at 5:34 pm

    lol

    Reply

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