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b) A box I contains 3 red balls,2 black and 1 white balls. Box II contains 1 red, 1 black ball and 3 white balls, Box III contains 3 red, 3 black balls and 3 white balls. A box is chosen at random and a ball is drawn, if it is from box I, what is the probability that it is i) Red ii) Black iii) White
2
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a ) A continuous Random variable has the p.d.f f(x)=Kxe−λx, if x≥0, λ≥0 =0 otherwise Determine i) K ii) The mean iii) variance.
b) A student takes a true false examination consisting of 8 questions. He guesses each answer. The guesses are made at random. Find the smallest value of n that the probability of guessing at least n correct answers is less than 1 / 2.
3. a)If the variance of a Poisson variate is 3. Find the probability that i) P(x=0) ii) P(1≤x<4) iii) P( x > 2)
b) 800 students appear for an examination. It was found that the marks are normally distributed with mean 60 and standard deviation 12. The students who get more than or equal to 60 will be placed in 1st division, who get between 50 and 60 will be placed in 2nd division, who get between 40 and 50 in 3rd division, who get more than 75 in distinction and who get less than 40 will be failed. Find the number of students who get i)1st division ii) 3rd division iii) Failed
4. a) A sample of 50 items is taken from a population whose standarddeviation is 12. The mean of the sample is 68. Construct 95% confidence interval.
b) A random sample of size 225 is taken whose mean is 80. Can this be regarded as a sample from a population with mean weight 82 and standard deviation 15.
5.a) Write about critical region and level of significance.
b) During a countrywide investigation the incidence of tuberculosis was found to be 3% in a college 700 strength. 5 reported to be effected in another sample of 1000 strength. Test the significance between the difference of two proportions at 5% level.
Cont…2
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::2::6. 200 digits were chosen at random from a set of tables. The frequencies of the digits are
digits 0 1 2 3 4 5 6 7 8 9
Frequency 18 19 23 21 16 25 22 20 21 15
Use χ2 test to assess the correctness of hypothesis that the digits were distributed in equal numbers in the table.
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Calculate the coefficient of correlation and the two lines of regression between the two variables x and y.8. a) Write about components of Time series. b) Write about characteristics of control charts.
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x 14 16 17 18 19 20 21 22 23
