Scribd
Upload
98 views2 pages

2071stat PDF

1. Brave's theorem deals with computing probabilities when outcomes come from multiple sources at different rates. The question provides the rates products are received from three suppliers and the quality rates from each. It asks to compute the overall probability a product will meet specifications and the probability a specific product that meets specifications came from a certain supplier. 2. Point estimation estimates a single value for a population parameter while interval estimation provides a range of plausible values. A good estimator is unbiased, consistent, and efficient. The sample mean is shown to be an unbiased and consistent estimator of the population mean. Given additional information, a 95% confidence interval is set up to estimate the population mean. 3. Karl Pearson's correlation coefficient

Uploaded by

sabi khadka
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
98 views2 pages

2071stat PDF

1. Brave's theorem deals with computing probabilities when outcomes come from multiple sources at different rates. The question provides the rates products are received from three suppliers and the quality rates from each. It asks to compute the overall probability a product will meet specifications and the probability a specific product that meets specifications came from a certain supplier. 2. Point estimation estimates a single value for a population parameter while interval estimation provides a range of plausible values. A good estimator is unbiased, consistent, and efficient. The sample mean is shown to be an unbiased and consistent estimator of the population mean. Given additional information, a 95% confidence interval is set up to estimate the population mean. 3. Karl Pearson's correlation coefficient

Uploaded by

sabi khadka
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 2

Group A – Attempt any Two: [2 X 10 = 20]

1. Explain Brave?s Theorem. Suppose that an assembly plant receives its voltage regulators from
three different suppliers, 60% from suppliers B1, 20% from supplier B2, and `10% from supplier
B3. If 95% of the voltage regulators from B1, 80% of those from B2, and 65% of those from B3
perform according to specifications, compute the probability that any one voltage regulator
received by the plant will perform according to specifications. Also obtain the probability that a
particular voltage regulator, which is known to perform according to specifications came from
supplier B3.

2. (a) Define point estimation and interval estimation. Explain the criteria that an estimator is
good. Show that the sample mean is an unbiased and consistent estimator of the population
mean.
(b) If x? = 60, S = 12, n = 50, and assuming that the population is normally distributed, set up a
95% confidence interval estimate of the population mean µ.

3. (a) Explain, for what purpose, Karl Pearson?s correlation coefficient is used in statistical
analysis? State its major properties.
(b) It has been realized that the production of coal in a certain coal factory has been affected to
some extent by the number of workers involved. The following table shows the production of
coal and the number of workers in a certain time during which the capital equipment remained
constant.

Output in tons (Y)

21

21

20

18171714

13

No of Workers (X)70686550474744

43

Utilizing the above data, fit a regression line of Y on X, and also predict Y for X = 60.

Group B. – Answer any eight questions: [8 X 5 = 40]


4. The following are the numbers of minutes that a person had to wait for the bus to work in a
local bus park of Kathmandu on 15 working days: 10, 1, 13, 9, 5, 9, 2, 10, 3, 8, 6, 17, 2, 10 and
15. Compute mean, median, mode, and explain about the shape of the distribution.

5. Define classical approach of probability. Explain conditional probabilities with suitable


examples.

6. Define Binomial probability distribution. If the mean of the binomial distribution is 3 and
standard deviation is 2, explain, whether this information is correct or not in the case of Binomial
distribution.

7. If two random variables have the joint probability density.

Find the conditional density of the first given that the second takes on the value x2.

8. Service calls come to a maintenance center according to a Poisson process and on the average
2.7 calls come per minute. Find the probability that no more than 4 calls come in any period.

9. Define normal probability distribution. Explain the important properties of normal


distribution.

10. Given a random variable having the normal distribution with µ = 16.2 and ? 2 = 1.5625, find
the probabilities that it will take on a value (i) greater than 16.8, (ii) less than 14.9, (iii) between
13.6 and 18.8.

11. Define Chi square distribution and its density function. Explain under which situation Chi-
square test is used in data analysis?

12. An importer is offered a shipment of machine tools for Rs 140,000, and the probabilities that
he will be able to sell them for Rs 180,000, Rs 170,000 and Rs 150,000 are 0.32, 0.55 and 0.13
respectively. What is the importer?s expected gross profit?

13. Write short notes on the following:

a)Properties of standard deviation


b) Principles of least square method

You might also like