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Problems and Solutions in Mathematical Finance: Stochastic Calculus, Volume I by Eric Chin, Sverrir Olafsson, Dian Nel

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1.2.2 Discrete and Continuous Random Variables

  1. 1. Bernoulli Distribution. Let c01-math-340 be a Bernoulli random variable, c01-math-341, c01-math-342 with probability mass function
    equation

    Show that c01-math-343 and c01-math-344.

    Solution

    If c01-math-345 then we can write

    equation

    and by definition

    equation

    and hence

    equation
  2. 2. Binomial Distribution. Let c01-math-346 be a sequence of independent Bernoulli random variables each with probability mass function

    and let

    Show that follows a binomial distribution, ...

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