Exercise 4 Solutions

Exercise 10.

In a sequence of Bernoulli trials let X be the length of run (of either successes or failures) started by the first trial.

  • Find the distribution of X, E(X), Var(X).
  • Let Y be the length of the second run. Find the distribution of Y , E(Y ), Var(Y ), and the joint distribution of X and Y

a

Exercise 12.

A group of 20 people consisting of 10 men and 10 women is randomly
arranged into 10 pairs of 2 each. Compute the expectation and variance of the number of
pairs that consist of a man and a woman. Now suppose the 20 people consist of 10 married
couples. Compute the mean and variance of the number of married couples that are paired
together.

Let be the event that the pair consist of a man and women.

Now let be the event that pair is a married couple
And lets redefine our indicator function and let be the random variable number of married couples

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