5.42Suppose that the probability distribution of a random variablexcan be described by the

formula

for each of the valuesp(x)=(x-3)2

55x= - 2, -1, 0, I, and 2.

Write the probability distribution ofx.

Show that the probability distribution ofxsatisfies the properties of a discrete probability distribution.

Calculate the mean ofx.

Calculate the variance and standard deviation ofx.