A farmer has six geese, each of which lays an egg with probability 2/3 (independently of all the other geese). Suppose that the farmer sells each egg for five gold coins. What is the variance of the number of coins received?

he number of eggs laid by each goose follows a binomial distribution since each goose lays an egg with a probability of 2/3 and there are 6 geese. The variance of a binomial distribution is given by the formula: Variance = n * p * (1 - p), where: n is the number of trials (geese in this case), p is the probability of success (laying an egg in this case). In this scenario, n = 6 (number of geese) and p = 2/3 (probability of laying an egg). Plugging these values into the formula: Variance = 6 * (2/3) * (1 - 2/3) = 6 * (2/3) * (1/3) = 12/9 = 4/3. Therefore, the variance of the number of coins received is 4/3.