A random sample of three numbers is selected from the number

A random sample of three numbers is selected from the numbers 1,2,3,4 and 5. let x be the largest of the three numbers.

a). construct the PMF of x as a table.

b). Find E(x)

Solution

no of ways we can select is ⁵C₃ ways =10

    sets are {1,2,3} {2,3,4} {3,4,5} {1,3,4} {1,3,5} {1,4,5} {2,3,5} {2,4,5} {1,2,5} {1,2,4}

pmf x :

L{1,2,3} =3            L{1,2,3} means larger number of the set

L{2,3,4} =4

L{3,4,5} =5

L{1,3,4} =4

L{1,3,5} =5

L{1,4,5} =5

L{2,3,5} =5

L{2,4,5} =5

L{1,2,5} =5

L{1,2,4}=4

b) E(x) = 6*5 +3*4+3/10 =45/10 =4.5