Question

In: Statistics and Probability

A gambler plays a sequence of games that she either wins or loses. The outcomes of...

A gambler plays a sequence of games that she either wins or loses. The outcomes of the games are independent, and the probability that the gambler wins is 2/3. The gambler stops playing as soon as she either has won a total of 2 games or has lost a total of 3 games. Let T be the number of games played by the gambler.

  1. Find the probability mass function of T.
  2. Find the mean of T.
  3. Find the standard deviation of T.

Solutions

Expert Solution

Answer:

Given that:

A gambler plays a sequence of games that she either wins or loses. The outcomes of the games are independent, and the probability that the gambler wins is 2/3.

The gambler stops playing as soon as she either has won a total of 2 games or has lost a total of 3 games

1. Find the probability mass function of T.

T can take possible values : 2, 3 and 4

As by the 4th game, either he would have won atleast 2 or lost atleast 3.

2. Find the mean of T.

3. Find the standard deviation of T.

orchestra answered 1 year ago
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