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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Roll a red die and a green die. Let the random variable be the larger of the two numbers if they are different and the common value if they are the same. (a) P(x=1) (b)P(x=4) (c) P(x<2) (d) P(3≤x≤6)
15. Sports Car Stripes How many different 4-color code stripes can be made on a sports car if each code consists of the colors green, red, blue, and white? All colors are used only once.
You have three red cards numbered 1,2,3 and two orange cards numbered 1,2. Finding the following probabilities
Exercise 9-22 Algo It is advertised that the average braking distance for a small car traveling at 65 miles per hour equals 120 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 37 small cars at 65 miles per hour and records the braking distance. The sample average braking distance is computed as 111 feet. Assume that the population standard deviation is 21 feet. (You may find it useful to reference the appropriate table: z table or t table) a. State the null and the alternative hypotheses for the test O Hg: H - 120; HA: p + 120 O Hg: P z 120; HẠ: P 120 b. Calculate the value of the test statistic and the p-value. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Test statistic 5 of 12 ! Next > - search prt sc home 144 2$ & 6 9 T Y U enter F G J K L pause C V alt ctri
A nuclear reactor becomes unstable if both safety mechanisms A and B fail. The probabilities of failure are P(A) =1/300 and P(B) = 1/200. Also, if A has failed, B is then more likely to fail: P(B/A)=1/100. a) What is the probability of the reactor going unstable? b) If B has failed, what is the probability of the reactor going unstable?
A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for the machine to work properly. Assume the probability of one part working does not depend on the functionality of any of the other parts. Also assume that the probabilities of the individual parts working are P(A) = P(B) = 0.95, P(C) = 0.91, and P(D) = 0.96. Find the probability that at least one of the four parts will work. Round to six decimal places.
prove that if random variables X and Y have same characteristic function, then have same distribution.
2 A random sample of size 12 drawn from a population of size 200. The sample values and their probabilities are (52,0.004), (72,0.003), (64,0.005), (58,0.003), (42,0.002), (76,0.006), (71,0.006), (63,0.006), (87,0.008), (57,0.002), (61,0.003) and (86,0.007). Estimate population total with a 95% confidence interval by using probability proportional to size sampling.
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).

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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