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A

Section A: Long Answer Questions

Attempt any TWO questions.

3 questions·10 marks each
1long10 marks

Define a probability distribution. Explain the binomial distribution with its mean and variance, and state the conditions under which it is applied.

probabilitydistribution
2long10 marks

Explain the normal distribution and its properties. The mean of a normal distribution is 50 and standard deviation is 10; find the probability that a value lies between 45 and 62.

normal-distribution
3long10 marks

What is hypothesis testing? Explain the procedure of testing of hypothesis including null and alternative hypotheses, level of significance, types of errors and the critical region.

hypothesis-testing
B

Section B: Short Answer Questions

Attempt any EIGHT questions.

9 questions·5 marks each
4short5 marks

State and explain the addition and multiplication theorems of probability with examples.

probability
5short5 marks

Explain the Poisson distribution with its mean and variance and state its applications.

poisson
6short5 marks

Define a random variable. Differentiate between discrete and continuous random variables with examples.

random-variable
7short5 marks

Define mathematical expectation. State and prove its properties.

expectation
8short5 marks

Explain the t-test for testing the significance of the difference between two sample means.

t-test
9short5 marks

Explain the z-test for a large sample test of a single mean with an example.

z-test
10short5 marks

Define Karl Pearson's coefficient of correlation and state its properties.

correlation
11short5 marks

What are regression coefficients? State their properties.

regression
12short5 marks

Explain the concept of sampling distribution and standard error.

samplingdistribution