Q1 If a random variable X takes the values

xk= [(-1)^k2^k] /k ; k=1,2,3....

with probabilities P^k= 2^-k . Find E(X).

Q.2 A man draws 2 balls from a bag containing 3 white and 5 black balls. If he is to receive

Rs. 50 for every white ball he draws and Rs. 20 for every black ball. Find his expectation.

Q.3 A and B throw an ordinary die alternately for a stake of Rs. 11, which is to be won by

one who first 6. Find their expectations, if A has the first chance.

Q.4 A publisher earns a profit of Rs. 20 on a book, if it is published at the right time, but the

profit earned is Rs. 18.00 if the publication is delayed. The profit is further reduced to Rs. 10.00 on each book, if through published in time or not published in time, if they are defective. If 20% of the books be defective and they are only 70% chances of publishing the book at the right time and in perfect conditions without any defect and 10% chances for not publishing in it right time and 20% chances are there a book not to be in the perfect condition. What is the publishers expected profit?

Q.5 A Card is drawn from a pack of 52 cards. If the value of faces cards 10, aces cards 1 and others according to denomination, find the expected value of the number of points on the card

Q.6 A person draws cards one by one from a pack until he draws all the aces. How many cards he may be expected to draw?

Q.7 A box contains 'a' white and 'b' balls. Find the expected value of the number of white balls drawn.

Q.8 A random variable X has a following p. d. f. {x/2 ; 0 < x < 2

Find (i) E(X) (ii)V(X) (iii)E(3X² - 2X)

Q.9 Let X be a random variable with E(X)= 10 and V(X)= 25. Find the positive values of a and b such that Y = aX - b has an expectation of 0 and variance of 1.