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1. If the joint probability distribution of X and Y is given by f(x,y) = (x^2 + y) / 134, for x = 2, 3, 4; y = 0, 1, 2, 3 find (a) P(Y < 2, X = 2) (c) P(X ? Y) (b) P(X ? 3, Y > 2) (d) P(X + Y = 6) Hint: It may help to make a table of the values of the probabilities. 2. Referring to Exercise 1, find (a) the marginal distribution of X; (c) the marginal distribution of Y. (b) When you add up all of the probabilities for the marginal distribution of X, do you get 1? (d) When you add up all of the probabilities for the marginal distribution of Y, do you get 1? 3. Referring to Exercises 1 and 2, find (a) The expected value of XY. (b) The expected value of X. (c) The expected value of Y. (d) The covariance of X and Y (COV(X, Y)). Round your final answer to 2 decimals. 4. Referring to Exercises 1 and 2, (a) Find the conditional distribution of X, given that Y = 2. (b) Find P(X ? 3 | Y = 2).

          1. If the joint probability distribution of X and Y is given by
f(x,y) = (x^2 + y) / 134, for x = 2, 3, 4; y = 0, 1, 2, 3
find
(a) P(Y < 2, X = 2) (c) P(X ? Y)
(b) P(X ? 3, Y > 2) (d) P(X + Y = 6)
Hint: It may help to make a table of the values of the probabilities.
2. Referring to Exercise 1, find
(a) the marginal distribution of X; (c) the marginal distribution of Y.
(b) When you add up all of the probabilities for the marginal distribution of X, do you get 1?
(d) When you add up all of the probabilities for the marginal distribution of Y, do you get 1?
3. Referring to Exercises 1 and 2, find
(a) The expected value of XY.
(b) The expected value of X.
(c) The expected value of Y.
(d) The covariance of X and Y (COV(X, Y)). Round your final answer to 2 decimals.
4. Referring to Exercises 1 and 2,
(a) Find the conditional distribution of X, given that Y = 2.
(b) Find P(X ? 3 | Y = 2).

1. If the joint probability distribution of X and Y is given by
f(x,y) = (x^2 + y) / 134, for x = 2, 3, 4; y = 0, 1, 2, 3
find
(a) P(Y < 2, X = 2) (c) P(X ? Y)
(b) P(X ? 3, Y > 2) (d) P(X + Y = 6)
Hint: It may help to make a table of the values of the probabilities.
2. Referring to Exercise 1, find
(a) the marginal distribution of X; (c) the marginal distribution of Y.
(b) When you add up all of the probabilities for the marginal distribution of X, do you get 1?
(d) When you add up all of the probabilities for the marginal distribution of Y, do you get 1?
3. Referring to Exercises 1 and 2, find
(a) The expected value of XY.
(b) The expected value of X.
(c) The expected value of Y.
(d) The covariance of X and Y (COV(X, Y)). Round your final answer to 2 decimals.
4. Referring to Exercises 1 and 2,
(a) Find the conditional distribution of X, given that Y = 2.
(b) Find P(X ? 3 | Y = 2).

Added by Antonio R.

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