Question

Determine the values of the random variables in each of the following distributions.

1. Two coins are tossed. Let H be the number of tails that occur. Determine the values of the random variable H.

of the random variable K representing the number of Koreans.

Answer 1

1) $P(H=0)=\frac{1}{2}*\frac{1}{2}=\frac{1}{4}.$

$P(H=1)=\frac{1}{2}*\frac{1}{2}*2=\frac{1}{2}.$

$P(H=2)=\frac{1}{2}*\frac{1}{2}=\frac{1}{4}.$

2) $P(K=0)=0.$

$P(K=1)=\frac{C_2^2*C_4^1}{C_6^3}=\frac{1}{5}.$

$P(K=2)=\frac{C_2^1*C_4^2}{C_6^3}=\frac{3}{5}.$

$P(K=3)=\frac{C_2^0*C_4^3}{C_6^3}=\frac{1}{5}.$