Problem #5: Suppose that X and Y have the following joint probability density function. f(x, y) = 56x, 0 < x < 7, y > 0, x − 4 < y < x + 4 Problem #5(a): Problem #5(b): (a) Find E(XY). (b) Find the covariance between X and Y. Round your answer to 4 decimals. Round your answer to 4 decimals.
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.(Sec. 3.2) A student is required to enroll in one, two, three, four, five, six on the desired courseload) at a local university. Let Y the number of classes the next student enrolls themselves in. The probability that y classes are selected is known to be proportional to y+1, in other words the pmf of Y is given by p(y) = k(y+1) for y 1,...,7, and 0 otherwise (a) What is the value of k? or seven classes (depending (b) What is the probability that at most four classes are enrolled in? (c) What is the probability that a student enrolls in between three and five classes (inclusive)? y? /40 for y 1,.,7 be the pmf of Y? Explain why why not (d) Could p(y) or1. Suppose X has probability function f(x)= x/6 x=1, 2, 3 Find g(y) if Y=X²
- Problem 2. (SW 11.8(a-c)) Consider the linear probability model Y₁ = Bo + B₁X₁ + U₁, and assume that E(u₂|X) = 0. (a) Show that Pr(Y; = 1|X₂) = Bo + B₁X₁. (b) Show that var(u₁|X;) = (B₁ + B₁X;)[1 − (B₁+ B₁X;)]. [Hint: You will need the formula for the variance of a Bernoulli variable, see, e.g., SW Equation (2.7).] (c) Is u heteroskedastic? Explain.3. Problem 3: Assume that the joint probability of X (receive values 1, 2) and Y (receives values 1, 2, 3) is represented by the following table Y 1 2 3 X 1 0.14 0.42 0.06 0.06 0.28 0.04 • Are X and Y independent? Compute E(X +Y) and E(XY).Two random variables X and Y have the following joint pdf: fxy(x, y) = = c(2x+y), 0, if 2 ≤ x ≤ 6 and 0 ≤ y ≤ 5 otherwise Find fx (r), fy (y), P(XProblem #8: Suppose that X and Y have the following joint probability density function. f(x, y) = 3y, 220: 0 0, x-2 < y < x+2 (a) Find E(XY). (b) Find the covariance between X and Y.12. You are given an easier way to compute covariance: Cov(X,Y)=E(XY)-E(X)*E(Y). Use this to compute the covariance of the following bivariate distribution: 0.2 0.1 0.1 1 0.2 0.1 0.1 0.21. Let X have the following density. Values of X -2 2 Probabilities 0.1 0.2 0.3 0.3 0.1 • (i) Derive E(X) and show all your steps. (ii) Derive E(X²) and show all your steps. (iii) Derive Std(X) and show all your steps.Problems 4.2. Suppose that X is a continuous random variable with probability density function given by f(x) = x² + x + } for 0If X is a continuous random variable and y = aX + b Prove that E ( Y ) = a E ( X ) + b and V ( Y ) = a² V ( X ) PROBLEM 1. %3D3) Find the mean and variance of the random variable X with probability function or density f(x). (a)f(x)={k(1-x), –15xs1 O otherwise (b) ƒ(x) = k/3× , x = 1,2,3,... Note: in this problem, you need to first find the values of k.SEE MORE QUESTIONSRecommended textbooks for youTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning