Question * Let X and Y be two random variables such that Cov(X,Y) =–3 . Then co(5X+3,-2Y-2)=-20 cov(-3X+5,-3Y+5)=-18 cov(3X+5,-2Y+5)=18 None of these
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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 3Q4/ Suppose there are two machines (A, B) in a factory, both producing chairs. Machine A produce twenty percent of their chairs and Machine B produce eighty percent of their chairs. fifteen percent of the chairs come from Machine A are defective and ten percent of the chairs come from Machine B are defective. If a chair is chosen randomly and found to be defective, what is the probability that it came from machine B?Assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.75 probability that a pea has green pods. Assume that the offspring peas are randomly selected in groups of 34. Is a result of 2 peas with green pods a result that is significantly low? Why or why not?
- A docs.google.com/forms/d/e (1) Let X be a random variable with p.d.f. fx) =- , then O.w (b) k- (0) k = (a) k=1 (d) k-5 (e) None of these a is the correct answer b is the correct answer c is the correct answer d is the correct answer e is the correct answer (2) Let X be a random variable with a function x= 0,1, 2,3 4 x! (3-x)! f(x) = , then p(x<1) is 0.w (b) (d) (e) None of these 27 (a) 27 (c) 27 a is the correct answer b is the correct answer c is the correct answer d is the correct answer e is the correct answerUrn A contains x red marbles and y white marbles, and urn B contains z red marbles and v white marbles. (i) If an urn is selected at random and a marble drawn, what is the probability that the marble is red? (ii) If a marble is drawn from urn A and put into urn B and then a marble is drawn from urn B, what is the probability that the second marble is red?20
- For independent random variables X and Y, we have var(X -Y) = var(X)-var(Y ). * true FalseConsider two urns: Urn-1 contains 3 red, 2 black and 4 white balls while Urn-2 contains 4 red, 4 black and 3 white balls. An urn is randomly selected with equal chances of it being Urn-1 or Urn-2, and then a ball is picked at random from the selected urn. (a) Find the probability that either a white or a red ball is picked? Your answer correct up to four decimal places. (b) If the picked ball is NOT black, find the probability it came from Urn-2? Your answer correct up to four decimal places.An analyst is presented with lists of 4 stocks and 5 bonds. He is asked to predict, in order, the 2 stocks that will yield the highest return over the next year and the 2 bonds that will have the highest return over the next year. Suppose that these predictions are made randomly and independently of each other. What is the probability that the analyst will be successful in at least 1 of the 2 tasks?
- 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 OIn a factory, in a batch of 100 products, there are on average 3 of defected ones. Probability of having the first defected product at the 10th(10.) product in 100 products.Question * Let X and Y be two random variables such that: Y = 75 – 3X – X², E(X²) = 12 and E(Y) = 54. suppose thatcov(X,Y) = -2, then E[(X + 1)2Y] = O None of these 160 428 66