1.)
2.)
3.)
4.)
a.)
i.) the samples should be drawn from the population randomly.
ii.) The size of the randomly drawn samples from the population should be equal to or greater than 30.
b.)
According to the Central limit Theorem(CLT ), the mean of the sampling distribution will be approximately equal to the mean of the population.
c.)
1. Draw the PDF for random variable X ~ N (ux, o3), marking clearly the location...
Prove that if random variable X follows a standard normal distribution (with mean u= 0 and standard deviation o = 1), then Y = X2 follows a chi-square distribution with 1 degree of freedom. In particular, show that My(t) = Mx2(t) = E[etX?), which equals the moment generating function of a chi-square distribution with 1 degree of freedom.
Practice problems using various statistical methods If n independent random variables X have normal distributions with means μ and the standard deviations σ , then determine the distribution of a. I. X-E(X) var(X) C. 2. If n independent random variables Xi have normal distributions with means μί and the standard deviations σί, then determine the distribution of a. b. Y -a1X1 + a2X2+ + anXn (ai constant) X-E(X) Vvar(X) 3. What is CLT? Proof briefly? What are t-, Chi-squared- and...
1. Consider a random experiment that has as an outcome the number x. Let the associated random variable be X, with true (population) and unknown probability density function fx(x), mean ux, and variance σχ2. Assume that n 2 independent, repeated trials of the random experiment are performed, resulting in the 2-sample of numerical outcomes x] and x2. Let estimate f x of true mean ux be μΧ-(X1 + x2)/2. Then the random variable associated with estimate Axis estimator Ax- (XI...
Dr. Beldi Qiang STATWOB Flotllework #1 1. Let X.,No X~ be a i.İ.d sample form Exp(1), and Y-Σ-x. (a) Use CLT to get a large sample distribution of Y (b) For n 100, give an approximation for P(Y> 100) (c) Let X be the sample mean, then approximate P(.IX <1.2) for n 100. x, from CDF F(r)-1-1/z for 1 e li,00) and ,ero 2Consider a random sample Xi.x, 、 otherwise. (a) Find the limiting distribution of Xim the smallest order...
Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normas For the population of healthy female adults, suppose the mean of the x distribution is about 4.76. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient's doctor are as follows. 4.9...
(b) For n = 100, give an approximaation for P(Y> 100) (c) Let X be the sample mean, then approximate P(1.1< 1.2) for -100. 2. Consider a random sample XX from CDF F(a) 1-1/ for z [1, 0o) and zero otherwise. (a) Find the limiting distribution of XiI.n, the smallest order statistic. (b) Find the limiting distribution of XI (c) Find the limiting distribution of n In X1:m- 3. Suppose that X,,, are iid. N(0,o2). Find a function of T(x)x...
- 07 sampling 's for review-SET 1 FOR POSTING.pdf 0 3 . 12 QUESTION 1 - TESTING WEATHER STATIONS FOR MARS A company has signed a contract to develop a "weather station” for use on Mars. It will continually measure temperature and wind speed. It must work in extreme cold and in the presence of fine dust, for one Martian year. The company wants to test its design, by building several prototypes, and subjecting the prototypes in a lab to...
Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with o = 2.9%. A random sample of 10 bank stocks gave the following yields (in percents). 5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1 The sample mean is x = 5.38%. Suppose that for the entire stock market, the mean dividend yield is u = 5.0%. Do these data indicate that the dividend yield of all...
Question 1 (0.5 points) A random variable X follows a normal distribution with mean of 50 and standard deviation of 5. Suppose we take a simple random sample of size 6 from the population above. Can we calculate the probability that the sample mean is between 45 and 60? (You do not need to actually calculate the probability for this question.) Yes, and the calculated probability would be exact. Yes, and the calculated probability would be approximate. No. Question 2...
Need help on how to get the answer. Thanks Problem 9: Suppose random variable X follows a normal distribution, with a mean of 3 and a standard deviation of 2. c) What is the approximate 85th percentile of X? answer:z = 1.04, so x = 3 + 2*1.04 = 5.08