Example 7-2: Central Limit TheoremSuppose that a random variable X has a continuousf(x)=/2, 4

Determine the distribution of the sample mean of the random sample of size n=40. The distribution of…

Answered: Example 7-2: Central Limit Theorem…

A First Course in Probability (10th Edition)

10th Edition

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Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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

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A continuous random variable X has the distribution function if X 3 Find K and f (x), P.d.f.
tion list estion 11 estion 12 estion 13 estion 14 estion 15 estion 16 estion 17 crunch A simple random sample of size n = 53 is obtained from a population that is skewed left with μ=77 and o=4. Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why? What is the sampling distribution of x? the sample size increases. OB. Yes. The central limit theorem states that only for underlying populations that are normal is the shape of the sampling distribution of x normal, regardless of the sample size, n. OC. No. The central limit theorem states that only if the shape of the underlying population is normal or uniform does the sampling distribution of x become approximately normal as the sample size, n, increases. OD. No. The central limit theorem states that regardless of the shape of the underlying population, the sampling distribution of x becomes approximately normal as the sample size, n, increases. What is the…
2b)
rom the set of numbers {4,6, 8}, a random sample of size 2 is selected with replacement. (a) Determine the sampling distribution of the sample mean X. (b) Find the mean E(X) of the sampling distribution of the sample mean X. Compare E(X) with the population mean u.
QUESTION 1 a) Let X₁, X2, X3,..., Xn be a random sample of size n from population X. Suppose that X follows an exponential distribution with parameter and Y = =-=1X₁. 19 iii) What is the value of sample size n, if P(|Y - 2n| < 40) ≥ 0.025? iv) Use the Central Limit Theorem to compute P(100
QUESTION 4 X - H Let X be a random variable and Z = be a function of X. a) Show that X has mean µ and variance o where Z~N(0, 1), b) Determine the parameters for X if P(X > 80)= 0.05 and P(X < 50)=0.10. c) If P(60 < X < k) = 0.5771, find k. %3D
Example 5-49. Let the p.d.f. of the random variable (x, y) be : a-² e-(x+y)/a ; x, y > 0, a > 0 f(x, y) = { , elsewhere Find the distribution of (X-Y).
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Example 7-2: Central Limit Theorem Suppose that a random variable X has a continuous uniform distribution: 1/2, 4sx56 f(x)=D 0, otherwise Find the distribution of the sample mean of a random sample of size n = 40.