MCA (Master of Computer Applications) Previous Year Question Paper

III Semester

Subject: Probability & Statistics

Time: 3 Hours

Max. Marks: 60

Note: Answer all questions.

Section A (4 x 10 = 40 Marks)

1. a) State and prove Baye's Theorem.
   b) Two dice are thrown. Find the probability of getting an even number on the first die or a total of 8.

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2. a) A random variable X has the following probability distribution:
   X: 0 1 2 3 4 5 6 7
   P(X): 0 k 2k 2k 3k k² 2k² 7k² + k
   Find (i) k (ii) Evaluate P(X < 6) (iii) P(0 < X < 5)
   b) Define Mathematical Expectation and explain its properties.

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3. a) Fit a Poisson distribution to the following data and test the goodness of fit.
   X: 0 1 2 3 4
   f: 123 59 14 3 1
   b) Explain the properties of Normal Distribution.
4. a) A population consists of five numbers 2,3,6,8,11. Consider all possible samples of size 2 which can be drawn with replacement from the population. Find
   

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   (i) The mean of the population
   (ii) The standard deviation of the population
   (iii) The mean of the sampling distribution of means.
   b) Explain about various types of errors in sampling.

Section B (4 x 5 = 20 Marks)

5. Explain about Scatter Diagram and its uses.

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6. Calculate Karl Pearson’s coefficient of correlation from the following data:
   X: 10 12 13 16 17 20 23 25
   Y: 9 13 10 14 15 18 21 24
7. In a partially destroyed laboratory record, only the lines of regression of y on x and x on y are available as 4x – 5y +7 = 0 and 16x – 3y – 5 = 0 respectively. Calculate the coefficient of correlation and the means of x and y.
8. A random sample of size 16 has 53 as mean. The sum of the squares of the deviations taken from mean is 150. Can this sample be regarded to have been taken from the population having 56 as mean? Obtain 95% and 99% confidence limits of the mean of the population.

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