Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find E(X).

Answer

N/a

Explanation

Number of ways of selecting any two positive integers from first six integers without repeating are `6xx5=30`.
Therefore the values of random variable `X` can be 2,3,4,5 or 6.
`P(X=2)=P` (selecting a number 2 and the other ess than 2)
`=P(1,2),(2,1)`
`2/30=1/15`
`P(X=3)=P` (selecting a number 3 and the other less than 3)
`=P[(1,3),(2,3),(3,1)` and `(3,2)]`
`=4/30=2/15`
`P(X=4)=P` (selecting a number 4 and the other less
`P[(1,4),(2,4),(3,4),(4,1),(4,2),(4,3)]`
`=6/30=3/15`
`P(X=5)=P` (selecting a number 5 and the other less than 5)
`=P[(1,5),(2,5),(3,5),(4,5),(5,1),`
`(5,2),(5,3),(5,4)]`
`=8/30=4/15`
`P(X=6)=P` (selecting a number 6 and the other less than 6)
`=P[(1,6),(2,6),(3,6),(4,6),(5,6),`
`(6,1),(6,2),(6,3),(6,4),(6,5)]`
`=10/30=1/3`
Therefore required proibability distribution is

`:.` Expectation of `X=E(X)=sumXP(X)`
`2xx1/15+3xx2/15+4x3/15+5xx4/15+6xx1/3`
`=(2+6+12+20+30)/15=70/15=14/3`