Q. 103.8( 4 Votes )

There are 4 cards numbered 1, 3 5 and 7, one number on one card. Two cards are drawn at random without replacement. Let X denote the sum of the numbers on the two drawn cards. Find the mean and variance of X.[CBSE 2017]

Answer :

Clearly, x can take values 4, 6, 8, 10, 12

We have


P(x = 4) = P [getting pair (1, 3) or (3, 1)]






P(x = 6) = P [getting pair (1, 5) or (5, 1)]






P(x = 8) = P [getting pair (1, 7) or (7, 1) or (3, 5) or (5, 3)]






P(x = 10) = P [getting pair (3, 7) or (7, 3)]






P(x = 12) = P[getting pair (7, 5) or (5, 7)]



.




Mean = ∑ xi P(xi)






= 8


Variance = E(x2) - [E(x)]2


.






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