What are the different methods of random sampling? Explain them briefly

Answer the following each question is of equal value:
1. Give the following two sets of data:
X: 4, 5, 9, 3, 7,9,12,15
Y: 12, 10, 9, 7, 7, 5, 4, 2
Find the correlation coefficient between X and Y.

2. Given the following sample data
21, 30, 15, 17, 18, 25, 30, 33, 17

a. Find the mean, median, and mode.
b. Compute the variance and standard deviation of the data set

3. Given that : P(A)=0.33; P(B)=0.55; P(A&B)=0.00

Find
a). P(Ac) b. P (A or B) c. P (A & B)c

4.(a) A population consists of 15 items, 10 of which are acceptable. In a sample of 4 items, what is the probability that exactly 3 are acceptable?

b. The number of America Idol has a mean of 29 million with a standard deviation of 5 million. Assume this distribution follows a normal distribution. What is the probability that next week’s show will have at least 23 million viewers?

5. a. What are the different methods of random sampling? Explain them briefly.

b. Briefly explain what is the central limit theorem