Download JNTUA MCA 2018 July Reg-Supply 1st Sem 9FBS101 Probability And Statistics Question Paper

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Code: 9FBS101

MCA I Semester Supplementary Examinations June/July 2018

PROBABILITY & STATISTICS

(For 2011 (LC), 2012, 2013, 2014, 2015 & 2016 admitted batches only)

Time: 3 hours Max. Marks: 60

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Answer any FIVE questions

All questions carry equal marks

1. Define conditional event, independent event and dependent event.
2. Three machines I, II, III produce 40%, 30%, of the total number of items of factory. The percentage of defective items of these machines are 4%, 2%, 3%. If an item is selected at random, find the probability that the item is defective.
3. A random variable X has the following probability distribution.
   

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   Values of x | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8
   P(x) | a | 3a | 5a | 7a | 9a | 11a | 13a | 15a | 17a
   (i) Determine the value of a. (ii) Find P(x<3), P(x=3). (iii) P(0<x<5).
4. Derive mean for normal distribution.
5. If a Poisson variate 2P(X=0) = P(X=2), find the probability that: (i) P(x < 3). (ii) P(2 < x < 5).

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6. A population consists of four numbers: 3, 4, 5 and 6. Consider all possible district samples of size 2 with replacement. Find: (i) Population mean. (ii) Population-standard deviation (SD). (iii) Sampling distribution of means (SDM).
7. The mean and standard deviation of a population are 225 and 278 respectively. What can be assert with 95% confidence about the maximum error if x = 225 and n = 100?
8. Construct 95% confidence interval for the mean in question (a).
9. The mean life of a sample of 10 electric bulbs (or motors) was found to be 1456 hours with standard deviation of 423 hours. A second sample of 17 bulbs (motors) chosen from a different batch showed a mean life of 1280 hours with standard deviation of 398. Is there a significant difference between the means of two batches? Also construct 95% confidence limits.
10. Give test statistic for: (i) t - test. (ii) f - test. (iii) ?² - test.

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11. From the following data, find whether there is any significant liking in the habit of taking soft drinks among the categories of employees.
    
    Employees
    Soft drinks | Clerks | Teachers | Officers
    Pepsi | 10 | 25 | 65
    

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    Thumsup | 15 | 30 | 65
    Fanta | 50 | 60 | 30
12. Find the least square regression equation of x₁ on x₂ and x₃ from the following data.
    x₁ | 3 | 15 | 6 | 8 | 12 | 14
    x₂ | 16 | 10 | 7 | 4 | 3 | 2
    

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    x₃ | 190 | 72 | 154 | 142 | 30 | 12

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