Example 17-3. Show thatIEx;(Ex;-1)]n(n-1)is an unbiased estimate of 0², for the samnple x1,X drawn on X which takes the values 1 or 0 with respective probabilities e and (1 – €).....

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Answered: Example 17-3. Show that2 is an unbiased…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Problem 1P

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show that if X11, X12,..., X1, X21, X22,..., X2n₂ are independent random variables, with the first n constitut- ing a random sample from an infinite population with the mean μ₁ and the variance of and the other n2 constitut- ing a random sample from an infinite population with the mean μ2 and the variance o2, then 1 M2 (a) E(X₁-X₂) = μ₁ −μ2; 07 0 22 (b) var(X₁-X₂) = + n₁ n₂
7.2.3. X is the continuous uniform (-5, 5) random variable. Given the event B = {|X| < 3}, find the (a) conditional PDF, fx|B(x), (b) conditional expected value, E[X|B], (c) conditional variance, Var[X|B].
hoosing among several different estimators of 0, select one that is unbiased. Example 9.3: Let X₁, X2, ..., Xn be a random sample from a population mean and variance o². Show that the sample variance, - Σ(x₁ - x)² = n-1 is an unbiased estimator of o². 5²
5.5-9 a only
6. Show that 1 s2 E1(Xi – x)² is unbiased estimator of the population variance o? i=1 п-1
13. A continuous random variable is uniformly distributed between 200 and 220. a. What is the probability a randomly selected value will be greater than 215? b. What is the probability a randomly selected value will be less than 205? c. What is the probability a randomly selected value will be between 205 and 215? a. P(x > 215) = (Simplify your answer.) b. P(x< 205) = (Simplify your answer.) c. P(205
3. An integer is randomly chosen from the set 1, 2,..., 100. If this integer is divisible by 2 we let Y = 0, and if it is not divisible by 2 but is divisible by 3 then Y = 1. We let Y = 2 in all other cases. Find mean and variance of Y.
Suppose that 320 random sample of size 15 are generated from an N(90,9) distribution and the associated 95% CI is calculated for each sample. How many of these 320 intervals would you expect to contain the true mean μ=90?
Assume that you have a sample of n,8, with the sample mean X, 42, and a sample standard deviation of S, 4, and you have an independent sample of n₂-15 from another population with a sample mean of X₂=34 and a sample standard deviation of S₂-5. What assumptions about the two populations are necessary in order to perform the pooled-variance t test for the hypothesis H:1P2 against the alternative H₁: pp and make a statistical decision? Choose the correct answer below A. It is necessary to assume that the populations from which you are sampling have independent normal distributions and equal variances. B. It is necessary to assume that the populations from which you are sampling have equal population means and positive standard deviations. OC. It is necessary to assume that the populations from which you are sampling have negative ISTAT fest statistics and unequal sample means. OD. It is necessary to assume that the populations from which you are sampling have unequal variances and equal…
3. An urn contains exactly 10 red chips and 6 blue chips. Five chips are randomly selected without replacement. Let X denote the number of blue chips in the sample of five chips. (a) What type of random variable is X? Indicate both the type and the appropriate parameters using the "~" notation. Write down the pmf of X, and do not forget to indicate the range of values that x can take on. X ~ px (x) (b) What is the probability that there are between two and four blue chips among the five chosen chips? Express your answer as a decimal. = (*)*
9. Let X₁, X2, ..., X5 be a random sample from a distribution with mean and variance 5 X₁, find Cov(X₁, X) 2. If X= = i=1

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Example 17-3. Show that2 is an unbiased estimate of 02, for the sample x1, X X drawn on X which takes the values 1 or 0 with respective probabilities e and (1 – n(n-1) e).