Assume a population of 3, 4, and 11. Assume that samples of size n=2 are randomly selected with replacement from the population. Listed below are the nine different samples. Complete parts a through d below.

3,3 3,4 3,11 4,3 4,4 4,11 11,3 11,4 11,11

a. Find the value of the population standard deviation.

(Round to three decimal places as needed.)

b. Find the standard deviation of each of the nine samples, then summarize the sampling distribution of the standard deviations in the format of a table representing the probability distribution of the distinct standard deviation values. Use ascending order of the sample standard deviations.

c. Find the mean of the sampling distribution of the sample standard deviations.

d. Do the sample standard deviations target the value of the population standard deviation? In general, do sample standard deviations make good estimators of population standard deviations? Why or why not?

A. The sample standard deviations do not target the population standard deviation, therefore, sample standard deviations are biased estimators.

B. The sample standard deviations do target the population standard deviation, therefore, sample standard deviations are unbiased estimators.

C. The sample standard deviations do not target the population standard deviation, therefore, sample standard deviations are unbiased estimators.

D. The sample standard deviations do target the population standard deviation, therefore, sample standard deviations are biased estimators

-24 4.50 Given that the probability that A occurs is 3, ities the probability that B does not occur is .6, and the probability that either A or B occurs is .5, find: (a) The probability that A does not occur. (b) The probability that both A and B occur. (c) The probability that A occurs and B does not occur. 4.51 The medical records of the male diabetic patients reporting to a clinic during one year provide the following percentages. Light Case Serious Case ur hates inhe conan can be viewed using the axioms of set theory. theory" Exercises 1.5 1. Let u, v, and to be sets. By the pairing axiom, the sets (u; and (o. ) Using the pairing and union axioms, show that the set (u, D, to) exits 2. Let A be a set. Show that the pairing axiom implies that the set (A "3. Let A be a set. The pairing axiom implies that the set (A} exists. Using regularity axiom, show that A n {A} = 0. Conclude that A $ A. 4. For sets A and B, the set {A, B} exists by the pairing axiom. Let A Using the regularity axiom, show that A n {A, B) = 0, and thus BEA 5. Let A, B, and C be sets. Suppose that A E B and B E C. Using the regular axiom, show that C # A. [Hint: Consider the set {A, B, C). ] 6. Let A and B be sets. Using the subset and power set axioms, show that the set P(A) n B exists. 7/ Let A and B be sets. Using the subset axiom, show that the set A \\ B exists 8. Show that no two of the sets o, (0), (o, (Ol) are equal to each other.Question 2 (3 marks) The code below should implement a simple four state FSM which increments a 4- bit synchronous counter when the FSM is in state 2'b10. An asynchronous reset signal is used to force both the state machine and the counter to all zeros whenever it is high. Identify the major problem with this code when synthesized. Propose a solution to fix the problem. You can define a new control signal if necessary. module simple_fam(elk, reset, count); input reset, elk; output [3:0] count; reg [3:0] count: reg [1:0] state; reg [ 1:0] next; always @ (posedge elk or posedge reset) begin if (reset) begin state - 2'600. end else begin state