41. A pair of dice is thrown. Let Z₁ be the number shown on the first die and Z₂ be the number shown on the second die. Let X = Z₁ + Z₂ and Y = Z₁ Z₂. Find a. E(Z₁). b. E(Z2). c. E(X).

Y; = Bo + B1 X; + ɛ; (1.1)

Let R = Z27. Finda. N(<0>). b. N(<3>). c. N(<9>)

A bag contains 3 red balls, 2 yellow balls, 2 green balls. Suppose that you pick three balls at random (without replacement). Let R denote the number of red balls and Y the number of yellow balls. Find E(R²Y³).

The graph of the derivative f"(t) of f (t) is shown. Compute the total change of f(t) over the interval [2, 5]. 2.5 1.5 1 0.5 1 2 3 4 6 8 +co +uc

7.) d

Let ā = (–1,0,1), b = (0, 3, −1) and ₹ = (1, 2, —2). a. Find à x b. b. Find (a + b) x č. c. Find b x a. d. Find (ã × c) + (6 × ē). V V V V V

Let å = (- 2, 2, 3) and b = (3, 1, – 2). Find å x b. V

Assume that P(A)=0.7 and P(B) = 0.2. If A and B are independent, find P(A and B). O A. 0.14 O B. 0.90 Oc. 0.76 O D. 1.00 in

.3 , Ry* In y dy