suppose x is the mean of a random sample of size n=36 from the chi-squared distribution with 18 degrees of freedom. use the central limit theorem to approximate the probability P(16 < x < 20) ?
suppose x is the mean of a random sample of size n=36 from the chi-squared distribution...
6) (10pts) Let X be the mean of a random sample of size n-20 from the uniform distribution 6) U(0,1). Approximate P( 02: X sab ) Using the Central Limit Theorem
X denote the mean of a random sample of size 25 from a gamma type distribu- tion with a = 4 and β > 0. Use the Central Limit theorem to find an approximate 0.954 confidence interval for μ, the mean of the gallina distribution. Hint: Use the random variable (X-43)/?7,/432/25. 6. Let Yi < ½ < < }, denote the order statistics of a randon sample of size n from a distribution that has pdf f(z) = 4r3/04, O...
Let X be the mean of a random sample of size n = 75 from the uniform distribution on the interval (0,4), .e 0, otherwise. Approximate the probability P(1.84 < X 〈 2.16).
Let X be the mean of a random sample of size n = 75 from the uniform distribution on the interval (0,4), .e 0, otherwise. Approximate the probability P(1.84 < X 〈 2.16).
6. Basic Computation: Central Limit Theorem Suppose x has a distribution with a mean of 20 and a standard deviation of 3. Random samples of size n 36 are drawn. (a) Describe the x distribution and compute the mean and standard deviation of the distribution. (b) Find the z value corresponding to x = 19. (c) Find P(x < 19). (d) Interpretation Would it be unusual for a random sample of size 36 from the x distribution to have a...
Problem (Modified from Problem 7-10 on page 248). Suppose that the random variable X has the continuous uniform distribution f(R) 0, otherwise Suppose that a random sample of n-12 observations is selected from this distribution, and consider the sample mean X. Although the sample size n -12 is not big, we assume that the Central Limit Theorem is applicable. (a) What is the approximate probability distribution of Xt Find the mean and variance of this quantity Appendix Table III on...
For a continuous random variable, Y, prove that the sample variance converges to the population variance as n goes to infinity. Do not use the chi squared distribution in the answer. Chebyshev's inequality and the central limit theorem CAN be used
6. Let X1, . . . , Xn denote a random sample (iid.) of size n from some distribution with unknown μ and σ2-25. Also let X-(1/ . (a) If the sample size n 64, compute the approximate probability that the sample mean X n) Σηι Xi denote the sample mean will be within 0.5 units of the unknown p. (b) If the sample size n must be chosen such that the probability is at least 0.95 that the sample...
5. Do you agree with the first three statements below? If yes, justify briefly. If not, correct it. For the last part, describe in a paragraph. If X is the mean of a random sample of size n froma population with the mean μ and the variance σ2, then its sampling distribution is a normal with the mean μ and the variance σ-, Agree Disagree If S2 is the variance of a random sample of size n taken from any...
Let X1, X2, ..., X48 denote a random sample of size n = 48 from the uniform distribution U(?1,1) with pdf f(x) = 1/2, ?1 < x < 1. E(X) = 0, Var(X) = 1/3 Let Y = (Summation)48, i=1 Xi and X= 1/48 (Summation)48, i=1 Xi. Use the Central Limit Theorem to approximate the following probability. 1. P(1.2<Y<4) 2. P(X< 1/12)