X is a random variable. It is known that E[X] = 0. The experiment that generates X is run 5 times and 5 measurements of X are taken. They are: 12 13 25 -24.0 34.0 66.5 10.0 -8.4 The most plausible statement to be concluded from these facts is: a. X is continuous and uniform on (-2000, 2000) b. X always takes on integer values c. Var[X] > 4 d. X is orthogonal to X?

X is a random variable. It is known that E[X] = 0. The experiment that generates X is run 5 times and 5 measurements of X are taken. They are: 12 13 25 -24.0 34.0 66.5 10.0 -8.4 The most plausible statement to be concluded from these facts is: a. X is continuous and uniform on (-2000, 2000) b. X always takes on integer values c. Var[X] > 4 d. X is orthogonal to X?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

3. 3. A random variable that can be used to find a 0.954 confidence interval for μ, the mean of the gamma distribution is (F-4B) 5x = -10-t(n-1) √482/25 28 O True O False 4. 4. The confidence interval of ß is given by O True O False 5x 5 x (ਕਰ) (10 + ta) ´ 2 (10 − ta) -
6.1-5
- 8.2.11. Let X1, X2,..., Xn be a random sample from a distribution with pdf f(x; 0) 0-1, 0 0. Show the likelihood has mlr in the statistic II1X₁. Use this to determine the UMP test for Ho : 0 = 0' against H₁ : 0 0. Guniformly most powerful test
4.2.8: Let i denote the mean of a random sample of size n from a distribution that has mean u and variance o? = 10. Find n so that the probability is approximately 0.954 that the random interval (i -x +) includes u.
51. Let X1, X2, ., X25 be a random sample of size n from normal distribution with the expected value of u, variance a and i, = 45 ve E(x – žn)? = 2400 are observed from the sample. Which one of the following is the value of test statistics for testing the null hypotheis of Ho: H = 40 against the alternative Ha: u > 40. a) 2 b) 2.5 c) 1.25 d) 1.96 e) 1.375
6.19 Twelve trials are conducted in a Bernoulli process in which the probability of success in a given trial is 0.3. If x = the number of successes, determine the following: E(x) b. αx c. P(x = 3) d. P (2 ≤ x ≤ 8) e. P(x > 3)
2. Producer claims that the mean life time of a battery is 21, 5h. A sample of 6 batteries resulted in the following data: 19, 18 , 22 , 20, 16 , 25. Verify this claim versus the doubts of customers that (0 the lifetime is shorter. Put a = 0,01. [Ans. –1, 16 ¢ (-∞, -4, 03) ; we fail to reject the claim of the producer]
Having obtained a random sample from a population, you want to use a χ-squared test for determine whether the population distribution is standard normal. If you base the test on six class intervals that have equal probability, the second interval has the form (−.96743, b), in the next space write the value of b. Answer for part 1 b) If you want to use a χ-square test to prove H0: the population distribution is normal with μ = 0.5, σ = 0.002 and the test must be based on six class intervals Equally probable, the second interval has the form (0.4980652, b), in the next space write the value of b. Answer for part 2 c) Assuming that χ2 = 8.11 and α = 0.10 choose the correct option:
4.2.9. Let X₁, X2,..., X9 be a random sample of size 9 from a distribution that is N(μ, 0²). (a) Ifo is known, find the length of a 95% confidence interval for is based on the random variable √9(X -μ)/o. fl if this interval (b) Ifo is unknown, find the expected value of the length of a 95% confidence if this interval is based on the random variable √9(x-μ)/S. Hint: Write E(S) = (o/√n - 1)E[((n − 1)S²/0²)¹/2]. interval for fl (c) Compare these two answers.
The net weight in pounds of a packaged chemical herbicide is uniform for 49.75 < x < 50.25 pounds.Answer the following questions:a. Calculate the PDF, mean and variance of the weight of packages
Suppose there is a claim that a certain population has a mean, µ, that is less than 7. You want to test this claim. To do so, ybu collect a large random sample from the population and perform a hypothesis test at the 0.05 level of significance. To start this test, you write the null hypothesis, H, and the alternative hypothesis, H,, as follows. Ho: H=7 H: µ<7 Suppose you also know the following information. The value of the test statistic based on the sample is -1.995 (rounded to 3 decimal places). The p-value is 0.023 (rounded to 3 decimal places). (a) Complete the steps below for this hypothesis test. Standard Normal Distribution 0.4 Step 1: Select one-tailed or two-tailed. O One-tailed O Two-tailed 0.3- Step 2: Enter the test statistic. (Round to 3 decimal places.) Subr
Page 223, 3.7.8