If x is a discrete random variable and 'a' is a constant show that
(i) E(a)=a
(ii) E(ax)=aE(x)
(iii) `E(x-barX)=0`

If a is a constant prove that (i) var(a)=0 (ii) var (aX)=a^(2)var(X) (iii) Var(ax+b)=a^(2)var(X)

Define a discrete random variable X and its mean E(x) and variance Var(x)

A discrete random variable X has the following distribution: find a.

prove that E(ax+b)=aE(x)+b where a and b are constants

Show that ,the maximum value of ((1)/(x))^(x) is e^((1)/(e)

Define the probability function of a discrete random variable x .state the conditions satisfied by it

Answer the following questions (Alternatives are to be noted): If x and y are both are negative random variables, mutually independent, E(xy) = 6 and |E(x)| = 2 , find E(Y) .

A random variable X has the following probability distribution:  Determine (i) K (ii) P(X lt 3)  (iii) P(X gt 6) (iv) P(0 lt X lt 3)

Answer the following questions (Alternatives are to be noted): For a random variable X, show that [E (x^2)]^(1/2) ge E(x) .

The variance of a random varibale x is defined by the expected value of (x-barx)^(2) where bar x is the mean of x prove that variance (x) = E(x^(2))-{E(x)}^(2)