1. Consider the following probability density function for random variable X
2. ()=(2+3); 03
3. Find the value of(2 marks)
4. Find the probability thatis between 1.25 and 2.62 (2 marks)
5. Consider the following probability distribution for random variable x
6. ()=22+3; =0,1,2
7. Find the value of(2 marks)
8. Compute[2 2](3 marks)
9. The early morning trading volumes (millions of shares) at Nairobi Securities Exchange for
10. a certain number of days in January are as shown below.
11. 2163, 1436, 2194, 1695, 1980, 2021, 2101, 1220, 1874, 2121, 2001, 1578, 1339, 2232, 1672, 2231, 2314, 1943, 1178

The probability distribution of trading volume is approximately normal. How many shares would have to be traded for the early morning trading volume for the company to be in the top 78%? (4 marks)

1. A discrete random variablehas the following probability distributions
2. Find(2 marks)
3. A machine fills containers with a particular product. Assume that the filling weights have a normal distribution. The standard deviation of filling weights from past data i s known to be 0.6 kgs. If only 15% of the containers hold at least 18 Kgs, what is the mean filling weight for the machine? (3 marks)
4. The following sets of data shows the mean marks of 35 interviewees from a certain job interview that was conducted by a HR Consulting Firm in Nairobi:
5. 23, 34, 69, 45, 79, 35, 47, 64, 34, 46, 31, 29, 49, 25, 45, 43, 39, 45, 22, 26, 28, 36, 42, 47, 32, 24, 58, 63, 72, 41, 55, 29, 34, 37, 71.
6. Use the systematic sampling method to select 9 samples with 39 as starting point and show the sampling distribution of mean for the selected samples (4 marks)