Let X be a discrete random variable with the following probability distribution: X = 0 | P(X = 0) = .1 X = 1 | P(X = 1) = .15 X = 2 | P(X = 2) = .2 X = 3 | P(X = 3) X = 4 | P(X= 4) = .2 X = 5 | P(X= 5) = .06 X = 6 | P(X= 6) = .04 (1) (2) %3D (3) %3D .25 (4) %3D (5) %3D 1.) Compute the Expected Value E(X) of X. 2.) Compute the Variance Var(X) of X. 3.) Compute the upper bound for the probability P(|X – E(X)| > 30)

4. Suppose that the random variable X has p.d.f. f(x) = { 1- |x – 1|, if 0 0.5. (c) Find the mean and variance of the random variable X.

The probability density function of a discrete random variable X is given by the following table: Px(X = 1) = .05 Px(X = 2) = .10 Px(X = 3) = .12 Px(X = 4) = .30 Px (X = 5) = .30 Px (X = 6) = .1i Px (X = 7) = .01 Px(X = 8) = .01 i) Compute E(X). ii) Compute Var(X). iii) Compute Px(X 3)

Which of the following tables represents a valid discrete probability distribution? X P(X=x) X P(X=X) X P(X=x) X P(X=x) 5 0.51 1 0.23 0 10 15 0.03 0.03 3 0.03 1 0.33 0.15 3 0.24 5 0.15 2 0.27 20 0.39 7 9 0.17 0.19 3 0.19 25 30 0.15 0.01 12 11 0.02 4 5 1.01 0.06 6 9 15 18 0.22 0.23 0.12 -0.03 0.43

(b) Two boxes each contain three cards. The first box contains cards labelled 1,3 and 5; the second box contains cards labelled 2,6 and 8. In a game, a player draws one card at random from each box and his score,is the sum of the numbers on the two cards (i) Obtain the probability distribution for the random variable X (ii) Calculate E[X],E[ X²]and variance of X (ii) Calculate the median and mode of X

Is the following distribution a probability distribution? (x, P(X)) = (-2,1.23); (-1, 0.15) ; (0, -1.20); (1, 0.52); (2, 0.30) There are five ordered pairs:  X values and their probabilities for example  P(1) = 0.52.   X -2 -1 0 1 2 P(X) 1.23 0.15 –1.20 0.52 0.30

Why is the probability that a continuous random variable equals a specific number zero?  That is, why is P(X=b)=0 for any number b?

You have given the following probability distribution for the discrete random variable X f(x) 1 0.1 2 0.3 3. 0.35 4 0.2 0.05 What is E(X) and V(X) ? E(X)=2.8 and V(X)=1.06 OE(X)=2.4 and V(X)=1.04 OE(X)-2.6 and V(X)-1.06 DE(X)=2.6 and V(X)-8.9 E(X)=2.8 and V(X)-8.9