3 In a large country 40 of people have type o blood 30 have

3. In a large country 40 % of people have type o blood 30% have type A. 25% have B. 5% have type AB Ten people are selected at random. Let X be the number with type O blood. Let Y be the number with type A blood. (a) Find Var (X+Y) (b) Find the correlation of X and y.

Solution

n = 10 people

X - no of people with O

Y - no of people with A

X is binomial with p = 0.4 n =10

Y is binomial with p = 0.3 n =10

x+y is binomial with p = 0.7 as there is no common between x and y

a) Var (x) = npq = 2.4

Var(Y) = 2.1

Hence Var(x+y) = 2.4+2.1 = 4.5

b) Correlation of x and y =0 as x and y are independent and no intersection between them

Bld group	A	B	AB	O
Percent	30	25	5	40