Calculate the mean and the variance of the hypergeometric distribution h(x;50,5,3).

Solution:

The mean of a hypergeometric distribution is given by: 

mean = (n * K) / N 

where n is the number of items to be drawn, K is the number of successful items in the population, and N is the total number of items in the population. 

For h(x;50,5,3), the mean is: 

mean = (3 * 5) / 50 = 0.3 

The variance of a hypergeometric distribution is given by: 

variance = (n * K * (N - K) * (N - n)) / (N^2 * (N - 1)) 

For h(x;50,5,3), the variance is: 

variance = (3 * 5 * (50 - 5) * (50 - 3)) / (50^2 * (50 - 1)) = 0.45 

So the mean of the hypergeometric distribution h(x;50,5,3) is 0.3 and the variance is 0.45.