Answer to Question #295057 in Statistics and Probability for gela vicente

Question

A shipment of five computers contains two

that slightly defective. If a retailer receives three of these computers at

random, list the elements of the sample space S using the letters D and N for

defective and non-defective computer, respectively. To each sample point assign a value x of the

random variable X representing the number of computers purchased by the

retailer which are slightly defective. FIND THE MEAN, VARIANCE AND STANDARD DEVIATION

Answer 1

$P(X=0)=\frac{C_3^0*C_2^2}{C_5^3}=\frac{1}{10}.$

$P(X=1)=\frac{C_3^1*C_2^2}{C_5^3}=\frac{3}{10}.$

$P(X=2)=\frac{C_3^2*C_2^1}{C_5^3}=\frac{3}{5}.$

$P(X=3)=0.$

$\mu=\frac{1}{10}*0+\frac{3}{10}*1+\frac{3}{5}*2=\frac{3}{2}=1.5.$

$\sigma^2=\frac{1}{10}*0^2+\frac{3}{10}*1^2+\frac{3}{5}*2^2-(\frac{3}{2})^2=\frac{9}{20}=0.45.$

$\sigma=\sqrt{0.45}\approx 0.67.$