3. State and prove the multiplication theorem for twoindependent random variables.Show that the mathematical expectation of productrUA DOr wo independent rändom variables is thẻ productof their expectations.OR

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Answered: 3. State and prove the multiplication…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The accompanying data are from an article. Each of 309 people who purchased a Honda Civic was classified according to gender and whether the car purchased had a hybrid engine or not. Male Female Hybrid 76 33 Not Hybrid 116 84 Suppose one of these 309 individuals is to be selected at random. Determine if the probabilities P(hybrid male) and P(male hybrid) are equal. If not, explain the difference between these two probabilities. O Yes, the probabilities are equal. No, the probabilities are not equal. The first is the probability that a hybrid Honda Civic owner is male, and the second is the probability that a male Honda Civic owner purchased a hybrid. O No, the probabilities are not equal. The first is the probability that a male Honda Civic owner purchased a hybrid, and the second is the probability that a hybrid Honda Civic owner is male.
Determine which of these statements is correct/incorrect and explain the reason why. a. X is a discrete random variable. Therefore, P(9 < X < 11) = P(X=9) + P(X=10) + P(X=11) b. The probability of flipping two coins will result in one head and one tail is 1/2 c. K and L are mutually exclusive events. P(K)=0.3 and P(L)=0.4. Hence, P(K∩L) = 0.12 d. There are mass points that have a probability of zero. That is, if x is a mass point, then it's possible that P(X=x) = zero.
Super D is a major video distributor that purchases blank SD Drives from two sources: Disk Makers, which provides 73% of the SD Drives, and Media Supply, which provides the remaining 27% . Historically,4% of the SD Drives Super D has purchased from Disk Makers have been defective, whereas 8% of the SD Drives purchased from Media Supply have been defective. A randomly selected SD Drive is found to be defective. Use Bayes' Theorem to determine the probability that the SD Drive came from Disk Makers.
3
A sign on the pumps at a gas station encourages customers to have their oil checked and claims that 1out of 7 cars need to have oil added. If this is true, what is:(a) The probability that 1 out of the next 4 cars need oil.(b) The probability that 2 out of the next 8 cars need oil.(c) The expectation and variance of the number of cars out of a total of 40 that need oil.
Show that the expectation of the sum of two random variables defined over the same sample space is the sum of the expectations. Hint: Let p1, p2, ··· , pn be the probabilities associated with the n sample points; let x1, x2, ··· , xn, and y1, y2, ··· , yn, be the values of the random variables x and y for the n sample points. Write out E(x), E(y), and E(x + y)
Consider the sample space {a,b,c,d,e} with probabilities, respectively, .1,.2,.3,.2,.2. Verify that this is a probability space. The random variable X is given by X(a)=1, X(b)=2, X(c)=3. X(d)=4 and X(e)=5. Compute the expected value and variance of X. Let X2 be two iterations of X, addeed, independently. Write down an appropriate probability space for this and compute the expected value and variance of X2 two different ways- directly from the probability space, and also by using our theorems, (If you think of X as the outcome of some game, then X2 is the result of playing the game twice, independently.)
Let 2 = {1,2, 3, 4, 5} be the sample space of a random experiment. Let also the events A = {1,2} and B = {2, 3, 4} be such that P(A N B) = 0.1, P(A) = 0.3 and P(B) = 0.8. Find the probabilities: (a) P({2}). (b) P({1}). (c) P(A°|B), (where Aº is the complement of A).
Select all that apply. Which is/are true of two-tailed tests? They are appropriate when it is not important to distinguish between no effect and an effect in either direction. They are more common than one-tailed tests. They compute two-tailed probabilities. They are more controversial than one-tailed tests.
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3. State and prove the multiplication theorem for two independent random variables. Show that the mathematical expectation of product of two independent random variables is the product of their expectations. OR