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. 2. A meeting of envoys was attended by 4 Koreans and 2 Filipinos. If three

envoys were selected at random one after the other, determine the values

of the random variable K representing the number of Koreans.

Answer 1

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

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

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

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

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

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

$P(K=3)=\frac{C_4^2*C_2^0}{C_6^3}=\frac{1}{5}.$