Download JNTUH MCA 1st Sem R17 2021 July-August 841AD Probability And Statistics Question Paper

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Code No: 841AD R17

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JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

MCA I Semester Examinations, July/August - 2021

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PROBABILITY AND STATISTICS

Time: 3 Hours Max.Marks:75

Answer any five questions

All questions carry equal marks

1. a) Two digits are selected at random from the digits 1 through 9.
   1. I) If the sum is odd, what is the probability that 2 is one of the digit selected.

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   2. II) If 2 is one of the digits selected, what is the probability that the sum is odd?
   b) A fair coin is tossed until a head or five tails occurs. Find the expected number of tosses of the coin. [8+7]
2. a) State and prove Boole’s inequalities b) A, B, C in order toss a coin. The first one to toss head wins the game. What are the probabilities of winning, assuming that the game may continue indefinitely? [7+8]
3. A continuous random variable X has the probability density function
   f(x):{Zx, if 0 0, otherwise
   

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   Find the cumulative distribution function for X.’Also find P(i
4. Find the probability of getting 1 or 4 or 5 or 6 in throwing a die 5 to 7 times among 9 trials using normal distribution. [8+7]
5. Show that for normal distribution the quartile deviation, mean deviation and standard deviation are approximately 10:12:15. [15]
6. a) Determine the mean and standard deviation of the sampling distribution of means of 300 random samples each of size 36 are drawn from a population of size 1500 which is normally distributed with mean 22.4 and standard deviation 0.048, if sampling is done
   1. I) with replacement and
   2. II) without replacement.
   b) Construct 95% confidence interval for the true proportion of computer literates if 47 out of 150 persons from rural areas are computer literates. [8+7]

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7. a) A normal population has a mean 0.1 and a standard deviation of 2.1. Find the probability that the mean of simple sample of 900 members will be negative. b) In a study conducted for 500 days, only on 4 days it was recorded that ‘lead’ content in a famous river exceeded 200mg/cm. Construct an upper 99% confidence limit for the probability that the ‘lead’ content in the river will exceed 200mg/cm on any one day. [7+8]
8. a) A briefcase manufacturing company claims that 80% of executives carried briefcases produced by them. Verify its claims if in a random sample of 900 executives, 675 used the company’s briefcases. Use 5% level of significance. b) Explain, stating clearly the assumptions involved, the t-test for testing the significance of the difference between the two sample means. [7+8]
9. The tangent of the angle between two regression lines is 0.6 and if ox= %Gy, find the correlation coefficient between x and y. [15]

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