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- 1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.6. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.6 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 1 Food C 1 1 2The joint pmf of X and Y is f(x, y) = 1/6, 0 ≤ x+y ≤ 2, where x and y are nonnegative integers. Compute Cov(X, Y) and determine the correlation coefficient.Make sure to show the correct work and solution: Suppose P(X = 0, Y = 0) = 1/3, P(X = 0, Y = 3) = 1/3, and P(X = 6, Y = 3) = 1/3. Find Cov(X, Y ) and the correlation ρ of X and Y .
- Suppose that Var(X) = 3, Var(Y ) = 4, and Cov(X,Y ) = 1. (a) Find Cov(2X −Y,X + 3Y ). (b) Find ρ(2X −Y,X + 3Y ) (the correlation between 2X −Y and X + 3Y ).If cov (x,y) = 0 is zero, then is ______ correlation. Select one: a. positive b. negative c. zero d. none of these Clear my choiceLet X and Y denote be as follows: E(X) = 10, E(X2) = 125, E(Y) = 20, Var(Y) =100 , and Var(X+Y) = 155. Let W = 2X-Y and let T = 4Y-3X. Find the covariance of W and T.