In an electronic system, a sensor measures a crucial parameter and outputs a number, but there is random error in its measurement. The measurement error in a sensor output is known to be RV X with uniform distribution in (-0.05,0.05) and independent from one output to the next, that is, the errors are iid! During a run of the system, n = 1000 samples of the sensor output are recorded. (a) Find the numerical value of the mean ux and the variance oź for the uniform distribution described. (You can use results in the text by listing the theorem or formula.) Further processing of these n= 1000 samples adds them together, and we are concerned about the overall error in the sum resulting from adding 1000 iid errors. Let X, denote the error in the įth sample for 1 1." Show all the steps in how you compute this. (f) Are the answers in (d) and (e) in agreement? If they are different, explain how both can be correct.

Determine if the following statement is true or false. the normal curve is symmetric about its​ mean, mu. choose the best answer below. a. the statement is false. the normal curve is not symmetric about its​ mean, because the mean is the balancing point of the graph of the distribution. the median is the point where​ 50% of the area under the distribution is to the left and​ 50% to the right.​ therefore, the normal curve could only be symmetric about its​ median, not about its mean. b. the statement is true. the normal curve is a symmetric distribution with one​ peak, which means the​ mean, median, and mode are all equal.​ therefore, the normal curve is symmetric about the​ mean, mu. c. the statement is false. the mean is the balancing point for the graph of a​ distribution, and​ therefore, it is impossible for any distribution to be symmetric about the mean. d. the statement is true. the mean is the balancing point for the graph of a​ distribution, and​ therefore, all distributions are symmetric about the mean.