2nd Year Statistics Notes

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• Write p.d.f. of standard normal distribution
• Find the value of maximum ordinate for a normal distribution with mean 25 and variance 16.
• If 𝑋~𝑁 40,49 , find median and standard deviation?
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• In a normal probability distribution, what are the first four moments about mean?
• Define normal frequency distribution.
• Write four properties of standard normal distribution. i. The distribution is bell shaped, unimodal and symmetrical. ii. In a normal probability distribution, the first four moments about mean are: iii. The total area under the normal curve is unity. iv. In a normal probability distribution: 
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• Define standard normal distribution. If the random variable X has a normal distribution with mean 𝜇 and variance 𝜎 2 , then the random variable z = (x - 𝜇)/ 𝜎 has a standard normal distribution with mean 0 and variance 1.
• 11- Define the point of inflexion in a normal distribution. The points of inflexion of the normal probability density function are equidistant from mean 𝜇, they are at x = 𝜇 – 𝜎 and x = 𝜇 + 𝜎.
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• Define normal frequency distribution. Ans: It is a continuous symmetrical, bell shaped distribution. Its mean, mode and median are all the same; and both the tails of the normal curve are infinitely long.
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• Define normal distribution? Ans: The normal distribution is the limiting from of the binomial distribution. when the number of trials in a binomial distribution is large and neither p (the probability of success) nor q (the probability of failure) is very small, then this distribution approaches a continuous distribution known as the normal distribution.
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• Explain sampling with replacement and without replacement? Ans: Sampling is said to be with replacement when the unit selected at random is returned to the population before the next unit is selected. Sampling is said to be without replacement when the unit selected at random is not returned to the population before the next unit is selected. 
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• In a normal distribution what are the values of 𝜇2𝑎𝑛𝑑 𝜇3?
• Define sample and sampling? 
• Explain sampling with replacement and without replacement?
• Define sampling distribution of means.
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• What is non-sampling error? 
• Explain the properties of the sampling distribution of a mean? 
• Define sampling error? 
• Write two advantages of sampling? 
• What is meant by bias?
• Explain the term non-sampling error. How it is reduced?
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• Explain what is meant by statistical estimation.
• Differentiate between point estimate and point estimator.
• Distinguish between null hypothesis and alternative hypothesis. 
• What are the assumptions of student’s t-statistics?
• What is meant by critical value?
• Express two properties of regression line. 
• Differentiate between regressor and regressand?  
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• Interpret the meaning when r = 0.
• Define simple linear regression.
• Explain the method of least square. 
• Define contingency table. 
• Give formulae for yule’s co-efficient of association.
• What is positive and negative association?
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• Whether the two attributes are attributes are independent or associated for the given data:
• Define analysis of time series.
• Write down main components of time series. 
• Define seasonal variations. 
• Write down four phases of a business cycle.
• Define the term secular trend. 
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• Define seasonal variation and give examples.
• Differentiate between hardware and software.
• What is secondary storage? Explain with examples.
• Define central processing unit (CPU). 
• What do you understand by ALU?
• Write down the names of different computers. 
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