∵ Two numbers are selected at random like {(2, 3) or (5, 4) or (4, 5)..etc}
Total ways of selecting two numbers without replacement = 6 x 5 = 30
As X denote the larger of two numbers selected
∴ X can take values 3, 4, 5, 6 and 7
P(X = 3) = P(larger number is 3)
![](https://www.sarthaks.com/?qa=blob&qa_blobid=2041506348755038401)
P(X = 4) = P(larger number is 4)
![](https://www.sarthaks.com/?qa=blob&qa_blobid=7768222421548513337)
P(X = 5) = P(larger number is 5)
![](https://www.sarthaks.com/?qa=blob&qa_blobid=10242522879138265410)
P(X = 6) = P(larger number is 6)
![](https://www.sarthaks.com/?qa=blob&qa_blobid=5762456790473629335)
P(X = 7) = P(larger number is 7)
![](https://www.sarthaks.com/?qa=blob&qa_blobid=5523891422077880262)
Now we have pi and xi.
Let’s proceed to find mean and variance.
Mean of any probability distribution is given by Mean = ∑xipi
Variance is given by:
Variance = ∑xi2pi – (∑xipi)2
∴ first we need to find the products i.e. pixi and pixi2 and add them to get mean and apply the above formula to get the variance.
Following table representing probability distribution gives the required products :
![](https://www.sarthaks.com/?qa=blob&qa_blobid=13961519850240893595)
![](https://www.sarthaks.com/?qa=blob&qa_blobid=1955564760834847212)