In the accompanying table the random variable x represents t

In the accompanying table, the random variable x represents the number of televisions in a household in a certain country. Determine whether or not the table is a probability distribution. If it is a probability distribution, find its mean and standard deviation. If the table is a probability distribution, what is its mean? Select the correct choice below and fill in any answer boxes within your choice. Its mean is (Round to the nearest tenth as needed.) The table is not a probability distribution. If the table is a probability distribution, what is its standard deviation? Select the correct choice below and 1 any answer boxes your Its standard deviation is (Round to the nearest tenth as needed.) The table is not a probability distribution.

Solution

Yes, the given table is a probability distribution. It follows a poisson distribution. So in poisson distribution mean = variance=lambda. Given X=0 to 5, n= 5. P(X)=[e^-lambda(lambda)^x]/x! ,so by putting x=0 in P(x), we get lambda=3.219. So mean = 3.219 and standard deviation=(3.219)=1.794.