JNTU
JNTU B.Tech II Year COMPUTER ORIENTED STATISTICAL METHODS Previous Question Paper (March - 2022 - R18)
Answer any five questions. All questions carry equal marks.
Main
In a certain college 25% of boys and 10% of girls are studying Mathematics. The girls constitute 60% of the students. If a student is selected and is found to be studying Mathematics, find the probability that the student is a:
i) Girl ii) boy
Answer
Let B be the event that the student is a boy and G be the event that the student is a girl. Let M be the event that the student is studying Mathematics. Given:
P(G) = 0.60, P(B) = 1 - 0.60 = 0.40
P(M|G) = 0.10, P(M|B) = 0.25
By the Law of Total Probability, the probability that a student is studying Mathematics is:
i) Using Bayes' Theorem, the probability that the student is a girl given they study Mathematics is:
ii) The probability that the student is a boy given they study Mathematics is:
If f(x) = Ke-x is p.d.f in -∞ ≤ x ≤ ∞, find:
i) K ii) the mean iii) Variance.
Answer
i) For f(x) to be a p.d.f., the integral over the entire range must equal 1:
Since the function is symmetric, we evaluate:
ii) The mean E(X) is defined as:
Since x e-|x| is an odd function, the integral over the symmetric interval (-∞, ∞) is 0. Thus, the mean is 0.
iii) The variance V(X) = E(X2) - [E(X)]2. Since E(X) = 0, V(X) = E(X2):
Therefore, the variance is 2.
There are three boxes: I contains 10 light bulbs (4 defective), II contains 6 light bulbs (1 defective), III contains 8 light bulbs (3 defective). A box is chosen at random and a bulb is selected. If it is defective, find the probability that it is from:
i) Box-I ii) Box-II iii) Box-III
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A continuous Random variable has the p.d.f f(x) = Kxλ-1e-x, for x ≥ 0, and 0 otherwise. Determine:
i) K ii) The mean iii) variance.
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The probability of a man hitting a target is 1/3. If he fires 6 times, find the probability of hitting:
i) At the most 5 times ii) At least 5 times
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The probabilities of a Poisson variate taking the values 1 and 2 are equal. Find:
i) μ ii) P(x ≥ 1).
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Assume that 50% of the Engineers are good in Mathematics. Find the probability that among 9:
i) Exactly 5 ii) At least 6
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If x is a Poisson variate such that 3P(x=4) = 1/2 P(x=2) + P(x=0). Find:
i) μ ii) P(x ≤ 2).
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Write the properties of normal distribution.
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Find the mean and variance of gamma distribution.
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The weekly wages of 1000 workers are normally distributed with mean Rs. 70 and a standard deviation of Rs. 5. If x is the weekly wages. Find:
i) P(68 < x < 72) ii) P(60 < x < 75)
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A random sample from a company's files shows that orders for a certain piece of machinery were filled in 10, 12, 19, 14, 15, 18, 11 and 13 days. Test the claim that on the average such orders are filled in 10.5 days. Test at 0.01 level.
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A candidate for election made a speech. Among 500 voters from city A 59.6% are in favour of him whereas among 300 voters from city B 50% are in favour of him. Test the significance between the differences of two proportions at 5% level.
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A random sample of size 500 was taken whose S.D is 6 and the mean is 40. Construct 95% confidence interval for the mean.
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A professor has three pet questions, one of which occurs on every test he gives. He never uses the same question twice in successive examinations. If he used the question no. 1, he tosses a coin and uses the question no. 2. If he uses the question no. 2, he tosses two coins and use the question no. 3, if both are heads. If he uses the question no. 3, he tosses three coins and use the question no 1, if all are heads. In long run which question does he use most often and with how much frequency is it used.
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