Question

two numbers are selected at random(wihtout replacement) from the first five integers.let x denote the larger of the two numbers obtain find the mean variance of x

Answer 1

HEY!!

The first five positive integers are 1, 2, 3, 4, 5.We can select the two positive numbers in 5**4 = 20 different ways.Out of this, 2 numbers are selected at random and let X denote the larger of the two numbers.

Since X is the large of the two numbers, X can assume the value of 2, 3, 4, 5.
P (X =2) = P (larger number is 2) = {(1,2) and (2,1)} = 230230
P (X = 3) = P (larger number is 3) = {(1,3), (3,1), (2,3), (3,2)} = 430430
P (X = 4) = P (larger number is 4) = {(1,4), (4,1), (2,4), (4,2), (3,4), (4,3)} = 630630

P (X = 5) = P (larger number is 5) = {(1,5), (51,), (2,5), (5,2), (3,5), (5,3), (4,5), (5.4)} = 830.

hope it helps