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) (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
7. (1 point) Let X be the mean of a random sample of size 36 from the uniform distribution U(7,15) Find P(11.3 <X < 11.5)
Let X, denote the mean of a random sample of size n from a distribution that has pdf (9xe-3x, x>0 f(x) = 0, otherwise Let Yn = mn (Ăn – ). Find the limit distribution of O N(0, 1) O N(0, 0) O N(o, ž) O N(0, 3) other
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 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)
(1 point) Let X1 and X2 be a random sample of size n= 2 from the exponential distribution with p.d.f. f(x) = 4e - 4x 0 < x < 0. Find the following: a) P(0.5 < X1 < 1.1,0.3 < X2 < 1.7) = b) E(X1(X2 – 0.5)2) =
Problem 5 Let Y1 denote the minimum of a random sample of size n from a distribution that has pdf f(x) e(,0x< o0, zero elsewhere X- n (Y1 0), find the cumulative distribution function (cdf) for Zn = n (Y1 - 0), and Let Zn find the limiting cdf of Zn as n >oo.
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...
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) ?