Consider a group of five potential blood donors a,b,c,d and e of whom only a and b have type O+ blood. Five blood samples, one from each individual will be typed in random order until an O+ individual is identified. Let Y be the random variable which represents the number of typings necessary to identify an O+ individual. Then which of the following statement (s) is (are) CORRECT? $\left(E\left(X\right)=\Sigma x_{i}P\left(X=x_i\right),E\left(X^2\right)=\Sigma {x_i}^{2}P\left(X=x_i\right)\right)$

P(1) = P (a or b typed first) =  $\frac{2}{5}=0.40$
P(2) = P (c, d or e first and then a or b)  $=\frac{3}{5}.\frac{2}{4}=0.30$
P(3) = P(c, d or e first and second, and then a or b) $=\left(\frac{3}{5}\right)\left(\frac{2}{4}\right)\left(\frac{2}{3}\right)=0.20$ 
P(4) = P(c, d or e first and second and third and then a or b)  $=\left(\frac{3}{5}\right)\left(\frac{2}{4}\right)\left(\frac{1}{3}\right)\left(1\right)=0.1$

i)  $E\left(X\right)=\sum _{i=1}^n{x}_{i}P(X=x_i)$
 $=\left(1\right)\left(0.40\right)+\left(2\right)\left(0.30\right)+\left(3\right)\left(0.20\right)+\left(4\right)\left(0.10\right)=2$
ii)  $E\left(X^2\right)=\sum _{i=1}^n{x}_i^{2}P(X=x_i)={\left(1\right)}^2\left(0.40\right)+\left(2^2\right)\left(0.30\right)+\left(3^2\right)\left(0.20\right)+\left(4^2\right)\left(0.10\right)$
 $=0.40+1.20+1.80+1.60=5$
iii)   $var\left(X\right)=E\left(X^2\right)-{\left(E\left(X\right)\right)}^2$
 $=5-{\left(2\right)}^2=5-4=1$
iv)  $\sigma \left(X\right)=\sqrt{\mathrm{var}\left(X\right)}=\sqrt{1}=1$