![about something, ask! Part .Do any eight (8) of 1-9 1. Two numbers are chosen at random in succession, with replacement, from the set 1, 2, 3, , 100J. What is the probability that the first one is larger than the second one? [15) 2. In a set of dominoes, each piece is marked with two numbers, one on each end. The pieces are symmetrical, so that the two numbers are unordered. (That is, you cant tell (1,4) and (4,1) apart.) We will consider dominoes formed using the numbers 0, 1,,12 in what follows a. How many different dominoes are possible? [5) b. If your set of dominoes has exactly one of each possible domino, what is the probability that the numbers on a randomly chosen domino add up to an odd number? [10 3. Let X be a continuous random variable with a standard normal distribution a. Verify that P(-2 < X < 2) 2 0.75. [5 b. Compute E (|X]). [10 4. Let X be a continuous random variable with probability density function f(x)ootherwise a. Determine the value of C. /5 b. Find the cumulative distribution function, F(x), of X. /8/ c. Find an interval a, b such that P(a < X b) 0.75. [2](http://img.homeworklib.com/questions/3a2edb80-83a7-11eb-a055-b1a6b4874156.png?x-oss-process=image/resize,w_560)
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about something, ask! Part .Do any eight (8) of 1-9 1. Two numbers are chosen at...
Problem 1 (35 points): Two numbers are chosen at random and simultaneously from among the numbers...
Problem 1 (35 points): Two numbers are chosen at random and simultaneously from among the numbers 1 to 4 without replacement. Let A,产(1,2,3,41, be the event that the first number is . 1. Find the probability of the event B that the second number chosen is 3. 2. What is the probability that the first number is 1 given that the second number is 3?
6th pls answer it fast robability Theory and Mathematical statistics Final examination Variant 4 Part 1....
6th
pls answer it fast
robability Theory and Mathematical statistics Final examination Variant 4 Part 1. Random Events he probability that a computer crashes during a severe thunderstorm is 0.005. A certain npany had 550 working computers when the area was hit by a severe thunderstorm. Compute ne probability that exactly 2 computers crashed. 2. It is known about random events A and B that PCB) = 5P (AB). PCA) = 0.7and P(A + B) = 0.6. Find P(B). 3....
Part 1 Suppose that 2 batteries are randomly chosen without replacement from a group of 12...
Part 1 Suppose that 2 batteries are randomly chosen without replacement from a group of 12 batteries: 3 new, 4 used (working), and 5 defective. Let the random variable X denote the number of new batteries chosen and the random variable Y denote the number of used batteries chosen. The joint distribution fxy is given in the following table: 0 12 17663/6 120/6612/66 1. Calculate P ( X 1 ,Y > 1) 2. Find the marginal probability mass function fx...
Find the appropriate measure of center. Discuss why the chosen measure is most appropriate. Why did...
Find the appropriate measure of center. Discuss why the chosen measure is most appropriate. Why did you decide against other possible measures of center? Find the appropriate measure of variation. The measure of variation chosen here should match the measure of center chosen in Part 1. Find the graph(s) needed to appropriately describe the data. These may be done by hand and inserted into the Word document. Define a random variable (X) so that your chosen data set represents values...
7. For a discrete random variable, the set of possible values is a. an interval of...
7. For a discrete random variable, the set of possible values is a. an interval of real numbers. b. a set of numbers that is countable. c. a set of numbers that has a finite number of numbers. d. none of the above. 8. Let X be a continuous random variable, then P( X = 0) is a. 0.00001. b. zero. c. can be large in some random variable. d. none of the above. 9. For a discrete random variable,...
8. Let X be a continuous random variable with mgf given by It< 1 M(t)E(eX) 1...
8. Let X be a continuous random variable with mgf given by It< 1 M(t)E(eX) 1 - t2 (a) Determine the expected value of X and the variance of X [3] (b) Let X1, X2, ... be a sequence of iid random variables with the same distribution as X. Let Y X and consider what happens to Y, as n tends to oo. (i) Is it true that Y, converges in probability to 0? (Explain.) [2] (ii) Explain why Vn...
Part 2. Random Variables 4. Two independent random variables Xand y are given with their distribution laws 0.3 0.7 0.8...
Part 2. Random Variables 4. Two independent random variables Xand y are given with their distribution laws 0.3 0.7 0.8 0.2 Pi Find the distribution law and variance for the random variable V-3XY 5. There are 7 white balls and 3 red balls in a box. Balls are taken from the box without return at randomm until one white ball is taken. Construct the distribution law for the number of taken balls. 6. Let X be a continuous random variable...
Ten students are chosen from a statistics class of 25. Let X be the number who...
Ten students are chosen from a statistics class of 25. Let X be the number who got an A in the class. Please answer yes or no to each part of the question. Yes No A fixed number of trials are conducted. If Yes - then n = _______? Yes No There are 2 possible outcomes for each trial. Yes No The probability of success is the same on each trial. Yes No The trials are independent or the sample...
Applied and Computational Questions 1. Pairs of random numbers (r, y) a. How many different pairs...
Applied and Computational Questions 1. Pairs of random numbers (r, y) a. How many different pairs are possible? are generated. X and Y are integers between 0 and 5 inclusive. a random variable W is defined to equal the absolute value of the difference between X b. Suppose and Y. How many distinct values are possible for W? Give the pair of dice is rolled once. 2. Let x represent the number of times a one appears when a probability...
4.60 The sum of two uniform random numbers. Generate two random numbers between 0 and 1...
4.60 The sum of two uniform random numbers. Generate two random numbers between 0 and 1 and take Y to be their sum. Then Y is a continuous random variable that can take any value between 0 and 2. The density curve of Y is the triangle shown in Figure 4.12. (a) Verify by geometry that the area under this curve is 1. (b) What is the probability that Y is less than 1? [Sketch the density curve, shade the...
Problem 1 (35 points): Two numbers are chosen at random and simultaneously from among the numbers 1 to 4 without replacement. Let A,产(1,2,3,41, be the event that the first number is . 1. Find the probability of the event B that the second number chosen is 3. 2. What is the probability that the first number is 1 given that the second number is 3?
6th
pls answer it fast
robability Theory and Mathematical statistics Final examination Variant 4 Part 1. Random Events he probability that a computer crashes during a severe thunderstorm is 0.005. A certain npany had 550 working computers when the area was hit by a severe thunderstorm. Compute ne probability that exactly 2 computers crashed. 2. It is known about random events A and B that PCB) = 5P (AB). PCA) = 0.7and P(A + B) = 0.6. Find P(B). 3....
Part 1 Suppose that 2 batteries are randomly chosen without replacement from a group of 12 batteries: 3 new, 4 used (working), and 5 defective. Let the random variable X denote the number of new batteries chosen and the random variable Y denote the number of used batteries chosen. The joint distribution fxy is given in the following table: 0 12 17663/6 120/6612/66 1. Calculate P ( X 1 ,Y > 1) 2. Find the marginal probability mass function fx...
7. For a discrete random variable, the set of possible values is a. an interval of real numbers. b. a set of numbers that is countable. c. a set of numbers that has a finite number of numbers. d. none of the above. 8. Let X be a continuous random variable, then P( X = 0) is a. 0.00001. b. zero. c. can be large in some random variable. d. none of the above. 9. For a discrete random variable,...
8. Let X be a continuous random variable with mgf given by It< 1 M(t)E(eX) 1 - t2 (a) Determine the expected value of X and the variance of X [3] (b) Let X1, X2, ... be a sequence of iid random variables with the same distribution as X. Let Y X and consider what happens to Y, as n tends to oo. (i) Is it true that Y, converges in probability to 0? (Explain.) [2] (ii) Explain why Vn...
Part 2. Random Variables 4. Two independent random variables Xand y are given with their distribution laws 0.3 0.7 0.8 0.2 Pi Find the distribution law and variance for the random variable V-3XY 5. There are 7 white balls and 3 red balls in a box. Balls are taken from the box without return at randomm until one white ball is taken. Construct the distribution law for the number of taken balls. 6. Let X be a continuous random variable...
Applied and Computational Questions 1. Pairs of random numbers (r, y) a. How many different pairs are possible? are generated. X and Y are integers between 0 and 5 inclusive. a random variable W is defined to equal the absolute value of the difference between X b. Suppose and Y. How many distinct values are possible for W? Give the pair of dice is rolled once. 2. Let x represent the number of times a one appears when a probability...
4.60 The sum of two uniform random numbers. Generate two random numbers between 0 and 1 and take Y to be their sum. Then Y is a continuous random variable that can take any value between 0 and 2. The density curve of Y is the triangle shown in Figure 4.12. (a) Verify by geometry that the area under this curve is 1. (b) What is the probability that Y is less than 1? [Sketch the density curve, shade the...
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