Question

1)A random variable is defined as 

  (a)Construct the Probability distribution function of X.

  (b) Compute;

     (i) the standard deviation of X            

  (ii) E                      

    (iii)Var

Answer 1

Let the mean of X be $\mu$

So, for the desecrate random variable (mean) $=\mu = E(x)$

Hence, $E(x)=\Sigma xP(x)$

Variance of X,

Var(X)=$\sigma^2=\Sigma X^2P(X) -\mu^2$

Standard deviation $(\sigma)= \sqrt{Var(X)}$