Question no 2)

A random variable takes the eight random samples given in the 7 7 matrix (where each value is in normalized form from 0 to 1):

0 3/7 2/7 2/7 1/7 1/7 4/7

3/7 2/7 1/7 1/7 1/7 1/7 4/7

2/7 0 1 1/7 3/7 0 0

0 5/7 1/7 0 6/7 0 1/7

1/7 1/7 1/7 3/7 6/7 6/7 5/7

1/7 1/7 1/7 1/7 5/7 6/7 4/7

0 1 0 0 0 0 4/7

Construct the probability mass function; estimate its mean and variance. Perform a goodness-of-fit test of the random samples of X to the Gaussian random variable with the estimated mean and variance. What is the relative frequency with which the null hypothesis is rejected at a 5% level?