Exercise 4.7

Answers

(a)

Let

R

be the birthrank of the chosen child. Then,

$P (R = 3) = \frac{20}{100} \frac{1}{3}$

$P (R = 2) = \frac{50}{100} \frac{1}{2} + \frac{20}{100} \frac{1}{3}$

$P (R = 1) = \frac{30}{100} + \frac{50}{100} \frac{1}{2} + \frac{20}{100} \frac{1}{3}$

$E (R) = 1 \frac{37}{60} + 2 \frac{19}{60} + 3 \frac{1}{5} = \frac{37}{20}$

$Var (R) = E (R^{2}) - {(E(R))}^{2} = \frac{221}{60} - \frac{1369}{400} \approx 0.26$

(b)

E (R) = \frac{100}{190} + 2 \frac{70}{190} + \frac{20}{190} = \frac{30}{19}

$Var (R) = \frac{56}{19} - {(\frac{30}{19})}^{2} \approx 0.45$

fifthist

2021-12-05 00:00