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QUESTION TWO: a) It is known from past experience that 80% of the students in a school do their homework. Find the probability that during a random check of ten students: i. all have done their homework ii. at most two have not done their homework iii. at least one has not done the homework iv. Find the expected number of students who do their homework. v. Find the standard deviation of students who do their homework. b) A population consists of the numbers 1, 3, 5, 7, and 9. i. List all possible samples of size two that can be drawn from the population without replacement. ii. Show that the mean of the sampling distribution of the sample means is equal to the population mean. iii. Calculate the variance of the sampling distribution of the sample mean and show that it is less than the population variance. c) Suppose that X is a discrete random variable with a probability mass function: P(x) = cx^2, x = 1, 2, 3, 4. i. Find the value of c. ii. Find E(X). iii. Find E[X(X-1)].

          QUESTION TWO:
a) It is known from past experience that 80% of the students in a school do their homework. Find the probability that during a random check of ten students:
     i. all have done their homework
    ii. at most two have not done their homework
   iii. at least one has not done the homework
   iv. Find the expected number of students who do their homework.
   v. Find the standard deviation of students who do their homework.
b) A population consists of the numbers 1, 3, 5, 7, and 9.
  i. List all possible samples of size two that can be drawn from the population without replacement.
 ii. Show that the mean of the sampling distribution of the sample means is equal to the population mean.
iii. Calculate the variance of the sampling distribution of the sample mean and show that it is less than the population variance.
c) Suppose that X is a discrete random variable with a probability mass function:
                 
                P(x) = cx^2, x = 1, 2, 3, 4.
     i. Find the value of c.
    ii. Find E(X).
   iii. Find E[X(X-1)].

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