Answer Happy

1. Suppose we have a sample about flexural strength (MPa) for concrete beams of a certain type: 5.9 7.2 7.3 6.3 8.1 6.8 7.0 7.6 The same study provides a second sample on strength observations for cylinders: 6.1 5.8 7.8 7.1 7.2 9.2 6.6 8.3 7.0 8.3 " Denote the sample of beam strengths by X1, ..., Xm and the sample of cylinder strengths by Y1, ... , Yn. The Xi's constitute a random sample from a distribution with mean Ji and standard deviation 01. The Yi's form a random sample (independent of the Xi's) from another distribution with mean uz and standard deviation 02. a. (5 points) Prove that X – 7 is an unbiased estimation of ui - M2. Calculate the value of this estimator based on the sample data we have. b. (5 points) Show the variance and standard deviation of estimator X – 7. Calculate the estimated standard deviation of X - 7 based on the sample data. (Hint: use sample variance to substitute population variance when necessary) - c. (5 points) Suppose a single beam X and a single cylinder Y are randomly selected. Calculate a point estimate of the variance of X - Y.