Question

1. The probabilities that Peter, Paul and Mary will go for a holiday this Christmas are 0.25, 0.3 and 0.4 respectively. If Peter goes for a holiday, Paul will not go but Mary will have a probability of 0.8 of going. Whether Paul goes or not, it does not affect Mary’s decision. Let x be the number of them going for a holiday this Christmas.
2. Find the probability distribution for x.
3. What are the mean and standard deviation of x?

Answer 1

2.

$P(3)=0.25\cdot0.3\cdot0.4=0.03$

$P(2)=0.25\cdot0.8+0.3\cdot0.4=0.32$

$P(1)=0.25+0.3+0.4=0.95$

3.

$\mu=E(X)=\sum p_ix_i=0.95\cdot1+0.32\cdot2+0.03\cdot3=1.68$

$\sigma=\sqrt{\frac{\sum (x_i-\mu)^2}{n}}=\sqrt{\frac{(1-1.68)^2+(2-1.68)^2+(3-1.68)^2}{3}}=0.877$