Question

(vi) If random variables X and Y are independent and E(X) = 0, E(Y) = 5, Var(X) = 10, then Cov(X, X – Y) is (a) 0, (b) 5, (c) 10, (d) none of these. (vii) E(XY) = E(X).E(Y) implies that the random variables X and Y are (a) independent, (b) uncorrelated, (c) linearly related, (d) none of these. 3. (a) Define random variable, its mean and its variance with an example. (b) For a random variable X, show that $[E(X^2)]^{1/2} \ge E(X)$. Hence show that mean deviation about mean cannot exceed standard deviation. 4. What do you mean by a discrete random variable and its probability distribution ? 5. A random experiment consists of three independent tosses of a fair coin. Write down the sample space. If X be the number of heads obtained, obtain the probability distribution of X, and calculate its expectation and variance. Find the expected gain of Hari, if he gains Rs. 16 from Ram for getting at least one head and loses Rs. 40 to Ram otherwise, when he tosses one unbiased coin thrice. 6. If X and Y are both negative random variables, mutually independent, E(XY) = 6 and E(X) = 2, find E(Y). 7. An unbiased die is thrown twice. Write down the sample space of this experiment. If X denotes the sum of points obtained in the two throws, obtain the probability distribution of X. 8. A bag contains 5 white and 3 black balls. 3 balls are drawn randomly without replacement. If X is a random variable, which takes value 1, if at least 2 white balls are drawn, and value 0, otherwise, find E(X).

          (vi) If random variables X and Y are independent and E(X) = 0, E(Y) = 5, Var(X) = 10, then Cov(X, X – Y) is
(a) 0, (b) 5, (c) 10, (d) none of these.
(vii) E(XY) = E(X).E(Y) implies that the random variables X and Y are
(a) independent, (b) uncorrelated, (c) linearly related, (d) none of these.
3. (a) Define random variable, its mean and its variance with an example.
(b) For a random variable X, show that $[E(X^2)]^{1/2} \ge E(X)$. Hence show that mean deviation about mean cannot exceed standard deviation.
4. What do you mean by a discrete random variable and its probability distribution ?
5. A random experiment consists of three independent tosses of a fair coin. Write down the sample space. If X be the number of heads obtained, obtain the probability distribution of X, and calculate its expectation and variance.
Find the expected gain of Hari, if he gains Rs. 16 from Ram for getting at least one head and loses Rs. 40 to Ram otherwise, when he tosses one unbiased coin thrice.
6. If X and Y are both negative random variables, mutually independent, E(XY) = 6 and E(X) = 2, find E(Y).
7. An unbiased die is thrown twice. Write down the sample space of this experiment. If X denotes the sum of points obtained in the two throws, obtain the probability distribution of X.
8. A bag contains 5 white and 3 black balls. 3 balls are drawn randomly without replacement. If X is a random variable, which takes value 1, if at least 2 white balls are drawn, and value 0, otherwise, find E(X).

(vi) If random variables X and Y are independent and E(X) = 0, E(Y) = 5, Var(X) = 10, then Cov(X, X – Y) is
(a) 0, (b) 5, (c) 10, (d) none of these.
(vii) E(XY) = E(X).E(Y) implies that the random variables X and Y are
(a) independent, (b) uncorrelated, (c) linearly related, (d) none of these.
3. (a) Define random variable, its mean and its variance with an example.
(b) For a random variable X, show that [E(X^2)]^1/2≥ E(X). Hence show that mean deviation about mean cannot exceed standard deviation.
4. What do you mean by a discrete random variable and its probability distribution ?
5. A random experiment consists of three independent tosses of a fair coin. Write down the sample space. If X be the number of heads obtained, obtain the probability distribution of X, and calculate its expectation and variance.
Find the expected gain of Hari, if he gains Rs. 16 from Ram for getting at least one head and loses Rs. 40 to Ram otherwise, when he tosses one unbiased coin thrice.
6. If X and Y are both negative random variables, mutually independent, E(XY) = 6 and E(X) = 2, find E(Y).
7. An unbiased die is thrown twice. Write down the sample space of this experiment. If X denotes the sum of points obtained in the two throws, obtain the probability distribution of X.
8. A bag contains 5 white and 3 black balls. 3 balls are drawn randomly without replacement. If X is a random variable, which takes value 1, if at least 2 white balls are drawn, and value 0, otherwise, find E(X).

Added by Debbie P.

Question

Please give Ace some feedback