Calculate the parameters of your group assessment: write the digits of your AUM student ID in the following table (D1 to D5): D1 D2 D3 D4 D5

D1 D2 D3 D4 D5

Student 1 5 6 8 5 8

Student 2 5 5 0 5 6

For example, if your AUM student ID is 34106, then D1=3, D2=4, D3=1, D4=0, D5=6.

Use only the numerical value of D1, D2, D3, D4, D5

Let N1 be the sum of AUM ID digits for the first student. Let N2 be the sum of AUM ID digits for the second student.

Let M be N1 + N2 + (2*8).

ID 1 59129 N1 = 26

ID 2 59599 N2 = 37

M = 26 + 37 + 2*5 = 73

Define P1, P2 and P3 as follows:

P1 = N1/M = 26/73 = 0.35 (round it to 2 decimal p.)

P2 = N2/M = 37/73 = 0.50 (round it to 2 decimal p.)

then P3 = 1 (0.35 + 0.5) = 0.15

A type of music player has three configurations: a model with 16 GB of storage, priced at 60 KD, a 32 GB model at 80 KD, and a 64 GB version with a price tag of 120 KD. The probability of purchasers choosing the 16 GB model is P1, to choose the 32 GB model is P2, and to choose the 64 GB model is P3 = 1 (P1 + P2).

1. Construct the probability distribution of the cost X.

Storage 16GB 32GB 64GB

Cost 60 KD 80 KD 120 KD

Probability P1= P2= P3=

Suppose that on a particular day only 4 music players are sold. Let X1 = the price from the first sale, X2 = the price of the second sale, X3 = the price of the third sale, and X4 = the price of the fourth sale. Suppose that X1, X2, X3 and X4 are independent, each with the calculated probability distribution. Then any possible 4-tuple (x1, x2, x3, x4) constitutes a random sample of size 4 from this distribution.

2) List all possible (x1, x2, x3, x4) 4-tuples.

3) Compute the probability of each 4-tuple using the above distribution.

4) Calculate the sample mean and sample variance values of all 4-tuples.

5) Find the probability distribution (sampling distribution) of the sample average for price, and plot the histogram of the calculated sample means.

6) Find the probability distribution (sampling distribution) of the sample variance for price, and plot the histogram of the calculated variances.

7) Calculate the expected value of all sample means and compare it with the theoretical value and explain whether they are similar or not and why.

8) Calculate the variance of all sample means (use software) and compare it with the theoretical value. Explain whether they are similar or not and why.

9) Calculate the expected value of all sample variances and compare it with the population variance. What do you observe about their relationship?

10) Calculate the probability that the sample mean is within one standard error from its expected value.