Suppose we have independent random variables Yi,...,Yn with ..... Y; = 0x; + ei, i = 1,...,n, iid where r1,..., In are fixed, known constants, 0 is a fixed but unknown parameter, and e; Normal (0, o?). a) What is the distribution of Y;? Are the Y;'s independent? b) Show that Yn/T is an unbiased estimator of 0 and calculate its variance. c) Show that (1/n) E1(Y:/x;) is an unbiased estimator of 0 and calculate its variance.

The weights of beagles (dogs) have approximately a normal distribution with u = 17.1 pounds and a standard deviation of o = 1.8 pounds. Suppose that we randomly select n = 64 beagles and measure their weights in pounds. Let X be the random variable representing the mean weight of the selected beagles. Let Xtot be the random variable representing the total weight of the selected beagles. a) About what proportion of beagles have weights between 17 and 18 pounds? b) About what proportion of beagles have weights greater 20 pounds? c) About how many of the 64 sampled beagles have weights less than 16.5 pounds? (nearest integer) d) About how many of the sampled beagles have weights between 17 and 18 pounds? (nearest integer) e) What is the standard deviation of the distribution of X? f) What is the standard deviation of the distribution of Xtot? g) What is the probability that 17 1100? f) Copy your R script for the above into the text box here.

3. If Z is a random variable having the standard normal distribution, find i. P(Z - 1.08) iii. P(-1.90

Here is true and false question   Thanks