Probability and Statistics

I. Let Xi, ,X, denote a random sample from a population with mean μ and variance σ2 Assume n 2. Consider the following two estimators (W, and Vo) for μ: (X1 + X2) 2 1-1 Find the relative efficiency of the second estimator compared to the first. Which estimator would you prefer based on this and why? 2. Find E(S2) and Var(S2) when X1, X2,… , Xn is a random sample from a normal distribution with mhean μ ad variance σ2. Is S2 a consistent estimate of σ2?

Let X1, . . . , Xn denote a random sample from a population with mean µ and variance σ 2 . Assume n > 2. Consider the following two estimators (Wn and Vn) for µ: EXPERT ANSWER

The compressive strength of concrete is tested by a civil engineer who tests 12 specimen and obtains the follow data, in psi: 2216, 2225, 2318, 2237, 2301, 2255, 2249, 2281, 2275, 2204, 2263, 2295. What is the 99% lower confidence bound on the mean strength?

The compressive strength of concrete is tested by a civil engineer who tests 12 specimen and obtains the follow data, in psi: 2216, 2225, 2318, 2237, 2301, 2255, 2249, 2281, 2275, 2204, 2263, 2295. What is the 99% lower confidence bound on the mean strength? EXPERT ANSWER Confidence interval for Population mean is given as …

The compressive strength of concrete is tested by a civil engineer who tests 12 specimen and obtains the follow data, in psi: 2216, 2225, 2318, 2237, 2301, 2255, 2249, 2281, 2275, 2204, 2263, 2295. What is the 99% lower confidence bound on the mean strength? Read More »

The compressive strength of concrete is tested by a civil engineer who tests 12 specimen and obtains the follow data, in psi: 2216, 2225, 2318, 2237, 2301, 2255, 2249, 2281, 2275, 2204, 2263, 2295. What is the sample mean of this data set?

The compressive strength of concrete is tested by a civil engineer who tests 12 specimen and obtains the follow data, in psi: 2216, 2225, 2318, 2237, 2301, 2255, 2249, 2281, 2275, 2204, 2263, 2295. What is the sample mean of this data set? EXPERT ANSWER

APPLYING THE CONCEPTS 2.15 The FIFA World Cup was one of the biggest sporting events of 2018. The file WC2018TeamAge contains the average age of the players (years, in 2018) of the 32 teams that qualified for the event. These average ages were: 26.04 26.78 21.17 27.57 28.17 28.43 28.61 28.96 26.09 27.09 27.26 27.78 28.22 28.43 28.78 29.17 26.09 27.09 27.26 27.83 28.26 28.52 28.83 29.52 26.48 27.09 27.48 28.09 28.35 28.35 28.91 29.74 4. Textbook, Problem 2.15, p.86. Use equal class width of 0.8 and start with 26.0. In addition, draw the corresponding frequency polygon. [Attention: There is a typing mistake in the average ages. It is 27.17 instead of 21.17.]

EXPERT ANSWER

The following data were used to construct the histograms of the number of days required to fill orders for Dawson Supply, Inc., and J.C. Clark Distributors. Dawson Supply Days for Delivery: 11 10 9 10 11 11 10 11 10 10 Clark Distributors Days for Delivery: 9 10 12 7 10 11 10 7 15 12 Dawson Supply Days for Delivery Frequency 10 11 ch Number of Working Days Clark Distributors Days for Delivery Frequency 10 12 11 13 14 Number of Working Days Calculate the range and standard deviation to support the previous observation that Dawson Supply provides the more consistent and reliable delivery times. Round your standard deviation to 2 decimal places. Dawson Supply Range 2 Standard deviation 0.64 3.C. Clark 8 Range Standard deviation 2.28

EXPERT ANSWER We have to find standard deviation of sample and not standard deviation of population.

Probability of outcome. Return.2 .04.3 .01.1 .08.4 .05

Stock AProbability of outcome. Return.2 .04.3 .01.1 .08.4 .05Stock BProbability of outcome Return.15 .02.25 .04.3 .03.3 .03(a) Calculate the expected return and variance for these two stocks and interpret the relationship between stock return and variance.(b) you want to form a portfolio consisting of 100 shares of each of two stocks above and the stock …

Probability of outcome. Return.2 .04.3 .01.1 .08.4 .05 Read More »