Download JNTUA MCA 2014 Aug Supple 1st Sem 06MC104 Probability And Statistics Question Paper

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Code: 06MC104

MCA I Semester Supplementary Examinations August 2014

PROBABILITY & STATISTICS

(For 2008 admitted students only)

Time: 3 hours Max. Marks: 60

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Answer any FIVE questions

All questions carry equal marks

1. (a) A and B throw alternatively with a pair of dice. One who first throws a total of nine wins. What are their respective chances of winning if A starts the game?
   (b) Define conditional probability. State and prove Baye’s theorem.
2. (a) (i) Define discrete distributive function.
   

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   (ii) Given that f(x) = k/2^x is a probability distribution for a random variable X that can take on the values x =0, 1, 2, 3 and 4. Find k, mean and variance of x.
   (b) (i) Define continuous distributive function.
   (ii) The cumulative distribution function for a continuous random variable X is F(x) = 1 - e^-2x; x = 0 then find density function f(x), mean and variance.
3. (a) It has been found that 2% of the tools produced by a certain machine are defective. What is the probability that in a shipment of 400 such tools:
   (i) 3% or more
   

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   (ii) 2% or less will prove defective.
   (b) List the properties of normal distribution.
4. (a) Find the mean and standard deviation of sampling distribution of variances for the population 2, 3, 4, 5 by drawing samples of size two
   (i) with replacement
   (ii) without replacement.
   

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   (b) What is the effect on standard error, if a sample is taken from an infinite population of sample size increased from 400 to 900?
5. (a) Prove that for a random sample of size 'n, x₁,x₂ — — — —x_n, taken from an infinite population S(x_i — x¯)² is not an unbiased estimator of the parameter s² but S(x_i — x¯)²/(n-1) is unbiased.
   (b) A random sample of size 100 is taken from a population with s = 5.1. Given that the sample mean is x¯ = 21.6, construct a 95% confidence interval for the population mean µ.
6. (a) In 64 randomly selected hours of production, the mean and the standard deviation of the number of acceptance pieces produced by an automatic stamping machine are x¯ = 1.038 and s = 0.146
   (b) In an investigation on the machine performance the following results are obtained.
   

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   No. of units inspected	No. of defectives
   Machine 1 375	17
   Machine 2 450	22

   Test whether there is any significant performance of two machines at a = 0.05.
7. (a) Explain student's t-distribution, its properties and applications.
   (b) The mean life time of a sample of 25 fluorescent light bulbs produced by a company is computed to be 1570 hours with a S.D of 120 hours. The company claims that the average life of the bulbs produced by the company is 1600 hours using the level of significance of 0.05. Is the claim acceptable?
8. (a) Write characteristics of (M/M/1): (8/FIFO) model.
   (b) What is queuing problem?

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