1. Explain the Gauss – Jordan Method for solving a system of linear simultaneous equation with the help of an example.
2. Coefficients of variation of two series are 75 percent and 90 percent, with standard deviations 15 and 18, respectively. a) Obtain the mean of the two series, b) Also comment which of the two is better represented by its mean.
3. Bottled sweet milk stored in a godown is reported to have gone sour. A test check revealed that milk in 25 percent of the bottles is unfit for consumption. The salesman at a retail outlet offers 5 bottles for sale on demand, find the probability that milk will be unfit for consumption a) exactly in 2 bottles, b) at least in 2 bottles, and c) at the most in 2 bottles.
4. A sample survey of tax-payers belonging to business class and professional class yielded the following results:
| Business class | Professional class | |
| Sample size | n1 = 400 | n2 = 420 |
| Defaulters in tax payment | x1 = 80 | x2 = 65 |
Test the hypothesis at α = 0.01 level of significance that defaulter rate is the same for the two classes of tax-payers.
5. Write short notes on:
i) Mixed Auto-regressive moving average models
ii) Least Squares Criterion
iii) Rank Correlation.
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