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Q.

Two dice A and B are rolled. Let the numbers obtained on A and B be αandβ respectively. If the variance of  αβ is pq, where p and q are co-prime, then the sum of the positive divisors of p is equal to

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a

72

b

48

c

36

d

31

answer is A.

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Detailed Solution

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E(X2)=x2P(X=x)=22536+3236+2736+1636+536=10518 E(X)=0 Now,σ2+(E(X))2=x2P(X=x) σ2=10518=356P=35 Sum of divisors =(50+51)(70+71)=48

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Two dice A and B are rolled. Let the numbers obtained on A and B be α and β respectively. If the variance of  α − β is pq, where p and q are co-prime, then the sum of the positive divisors of p is equal to