Q5 Suppose that X₁ and X₂ have a joint pdf zero otherwise. f(x₁, x₂) = (2/3)(x₁ + 1), for 0 < x₁ < 1,0 < x₂ < 1, Q5 (i.) Find fx₁ (₁) Q5 (ii.) Find fx₂(x₂) Q5 (iii.) Find P(X₁ < 2X₂ < 3X₁) Q5 (iv.) Are X₁ and X₂ independent? Q5(v.) Find Var (X₂) Q5 (vi.) Find a pdf of X₂/X₁. Q5(vi.) Find P(1/2 < X₂/X₁ < 3/2) using the pdf of X₂/X₁. Q5 (vii.) Find the conditional pdf of X₂ given X₁ = ₁, fx₂|X₁ (x₂|x₁). Q5 (viii.) Find E(X2|X1). Q5 (ix.) Find Var(E(X₂|X1)). Q(x.) Find E(Var(X₂|X₁)).

Use the second derivative test to find the local exterma of the function f(x) =x3+12x2-5 on R

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The point Q (-4,7) lies on the function f(x). Suppose f(x) is transformed according to: y=-3 f [0.5(x + 3)] + 5. Determine the x-coordinate of the transformed point, Q'. Enter only the x-coordinate, a single value, rounded correctly to 2 decimal places (ie 3.46 or 7.00 or 1.50)