Acan hit a target 4 times in 5 shots, B, 3 times in 4 shots; and C, 2 times in 3 shots. They fire a volley (it means one shot each). Find the probability that target will be hit.
[3 marks]Three companies A, Band Csupply 30%, 50% and 20% of the notebooks to a school. Past experience shows that 8%, 5% and 10% of the notebooks produced by these companies are defective. If a notebook was found to be defective, what is the probability that the notebook was supplied by A?
[4 marks]07 Arandom variable Xhas the following probability function X=x -2 -1 0 1 2 P(X=x) 0.1 K 0.2 2K 0.3 3K
[3 marks]Find K (ii) Find P(X<2) (iii) Determine the distribution function F(x) of X.
[ marks]Four balls are drawn simultaneously from a bag containing 6 white, 5 black and red balls. Find E(X), where Xdenotes number of white drawn.
[3 marks]It is known that the mean diameters of rivets produced by two firms Aand Bare practically the same, but the standard deviation may differ. For 22 rivets produced by firm A , the standard deviation is 2.9mm, while for 16 rivets manufactured by firm B, the standard deviation is 3.8mm. Compute the statistic you would use to test whether the products of firm Ahave the same variability as those of firm B. Using the value F (15,21) = 2.20 0.05
[4 marks]Fit a curve of the form 1/3 y = a b x to the following data x : 1 2 3 4 5 6 y : 87 97 113 129 202 195 193
[7 marks]Fit the second degree parabola using the least square method to the following data x : 1 2 3 y : 1.7 1.8 2.3 3.2
[4 marks]Find the mean and median for the given data C.I. 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 f 4 6 5 10 20 22 24 6 2 1
[3 marks]The first four moments of a distribution about the value 5 of the variate are 2, 20, 40, and 50. Find mean and variance.
[4 marks]Calculate the correlation coefficient between x and y using the following data x 1 2 3 4 5 6 7 8 9 y 9 8 10 12 11 13 14 16
[15 marks]State Chebyshev’s inequality. Afair dice is tossed 120 times. Use Chebyshev’s inequality to find a lower bound for the probability of getting 80 to 120 sixes.
[3 marks]Calculate the rank correlation coefficient for given data X 85 74 85 50 65 78 74 60 74 90 Y 78 91 78 58 60 72 80 55 68 70
[4 marks]The equation of two regression lines obtains in a correlation analysis of observations are 2/3 5 x = 6 y + 2 4 a n d 1 0 0 0 y = 7 8 6 x − 3 6 0 8 . What is the correlation coefficient? Show that the ratio of coefficient of variability of x to that of y is 5/24. What is the ratio of variance of x a n d y07 .
[ marks]Aspeaks truth in 75% cases and Bin 80% cases. Find the probability that they are likely to contradict each other in stating the same fact.
[3 marks]The incidence of occupational disease in an industry is such that the workmen have a 20% chance of suffering from it. What is the probability that out of 6 workmen or more will suffer from disease?
[4 marks]The following mistakes per page were observed in a book. No. of Mistake per page 0 1 2 3 4 Total No of Pages 211 90 14 5 0 320 Fit a Poisson distribution for the given data.
[7 marks]Suppose on an average 1 house in 1000 in a certain district has a fire during a year. If there are 2000 houses in that district, what is the probability that exactly 5 houses will have a fire during the year?
[3 marks]In a normal distribution 31% of the items are under 45 and 8% are over 64. Find the parameters of the distribution.
[4 marks]In a sample of 10 pens. If 10% of pens produced by a company are defective. Find out the probability that
[7 marks]Asample of 100 students is taken from a large population. The mean height of the students in this sample is 160 cm. Can it be reasonably regard that, in the population, the mean height is 165 cm and the SD is 10 cm? (use 5% level of significance)
[3 marks]Below are given the gain in weights (in lbs) of pigs fed on two diets Aand B. Gain in weight Diet A : 25, 32, 30, 34, 24, 14, 32, 24, 30, 31, 35, 25 Diet B : 44, 34, 22, 10, 47, 31, 40, 30, 32, 35, 18, 21, 35, 29, 22 Test if the two diets differ significantly as regards their effect on increase in weight. (using t at 25 d. f. = 2.07) 0.05
[4 marks]From the following table, test the hypothesis that the flower colour is independent of flatness of leaf07 Flat leaves Curled leaves Total White flowers 99 36 135 Red flowers 20 5 25 Total 119 41 160 If the value of 2 for 1 d. f at 5% level of significance is 3.841.
[ marks]Two large population, there are 30 % and 25 % respectively of blue eyed people. Is this difference likely to be hidden in the sample of 1200 and 900 respectively from the two populations? (Test at 5% level of significance).
[3 marks]Acertain stimulus administered to each of the 12 patients resulted in the following increase of blood pressure: 5, 2, 8, -1, 3, 0, -2, 1, 5, 0, 4 and Can it be concluded that the stimulus will, in general be accompanied by an increase in blood pressure? (Given that for 5% level of significance 3/3 t04 for 11 d. f is 1.796)
[6 marks]No pen must be defective. (ii) One must be defective. (iii) At least two must be defective.
[ marks]12 dice were thrown 4096 times and a throw of 6 was considered as a success; the observed frequencies were given below : No. of successes : 0 1 2 3 4 5 6 7 & above Frequencies 447 1145 1181 796 380 115 24 Find the value of chi-square on the basis of the hypothesis that the dice were unbiased and hence show that the data are consistent with the hypothesis so far as the 2 − test is concerned. The value of χ 207 for 7 degrees of freedom at 5% level of significance is 14.067.
[8 marks]