Suppose that the joint CDF of the random variables X and Y is given by: 0, x < -2 or y < -5 3/8, -2<< 2 and -5
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Q: 3. A) If X and Y are independent random variables with variances o variance of the random variable Z…
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- Q1:Show that: If X1, X2, , Xn are independent random variables and X = X1 + X2 ++Xn, then Q2: What is the expectation and the variance of RV X, where X represents the out come throwing a die? Q3: Find the expectation and the variance of X, where X is binomial random variable X - Binomial (n, p), Var(X)? 1 Chapter 3 Let X be a discrete random variable with range Rx = {1, 2, 3, ...}. Q4: Suppose the PMF of X is given by 1 for k = 1, 2, 3, ... 2k Px (k) = a) Find and plot the CDF of X, Fx (a). b) Find P(1 < X < 3). Chapter 3 Functions of Random Variables Q5: Example. Let Rx = {0, T T 37 , such that 4'2 4. Find E[sin(X)]. Q6: A machine produces a defected items with a probability of 0.1. What is the probability that in a sample of three item will have at most one item defected? Q7: For any independent X, and Y random variables, E[XY]=E[X]E[Y]. Show that? Q8: Suppose RV X has the following PMF: p(0)=0.2, p(1)=0.5, p(2)=0.3. Find E[X], E[X^2], E[X]^2. 3 Chapter 312Let Y be a binomial random variable with n = 10 and p = 0.3. (a) P(3 < Y < 5) = P(3 ≤ Y < 5) = (b) P(3 < Y ≤ 5) = P(3 ≤ Y ≤ 5) =
- Let X1, X2,..., X3 denote a random sample from a population having mean u and variance o?... Which of the estimators have a variance of 7 X1+X2++X, 7 2X1-X6+X4 2 3X1-X3+X4 2 2(X1+X2+.+X¬) 4 7The random variable X takes values -1, 0, 1 with probabilities 1/8, 3/8, 4/8 respectively. a) Write the CDF of X. b) Write the PMF of Y = X² + 2. %3D c) Compute E(Y).please send correct answer Q6
- 13) (3 points each) Suppose X and Y are independent random variables each having expected value 5 and standard deviation 3. Calculate d) If you were told that Cov(X,Y) = 4, and that X and Y are not independent, what would Var(X-Y) be?Suppose that X is a random variable * ? having the following m.g.f., Find Var(x) 7t_e4t M, (t) = eT 173 O 5 O 413 O 3148 O 55 OSuppose X, Y, and Z are three independent normal random variables. X has an expected value of 7 and a standard deviation of 2; Y has an expected value of -2 and a standard deviation of 4; Z has an expected value of 5 and a standard deviation of 12. Let T = 3X + 12Y - 2Z Variable X Y Mean(Expected Value) 7 -2 Standard Deviation 2 4 12 Coefficient 3 12 -2 a) What is the expected value of T? b) What is the variance of Z? c) What is the variance of T? d) What is the standard deviation of T? N LO