Not yet checked 4 of 8 questions have not yet been compared with the official paper.
Q. 1
(a)Write down empirical relation between mean, median and mode. [4]
(b)Find the median, quartiles and the 8 th decile for the distribution of examination marks given below: Marks 30-39 40-49 50-59 60-69 70-79 80-89 90-99 No of student 8 87 190 304 211 85 20 [16]
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Q. 2
(a)Describe the properties of standard deviation. [4]
(b)By multiplying each of the number 3,6,2,1,7,5 by 2 and then adding 5 we get 11,17,9,7,19,15 what is the relation between the standard deviation and the mean for the two sets. [8]
(c)The breaking strength of 20 test pieces of a certain alloy is given as under 95,103,97,130,96,73,78,95,89,68,82,79,69,67,83,108,94,87,93,117 Show that Mean deviation=(4/5)Standard deviation. [8]
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Q. 3
(a)Box A contains 5 green and 7 red balls. Box B contains 3 green,3 red and 6 yellow balls. A box is selected at random and a ball is drawn at random from it. What is the probability that ball drawn is green, [10]
(b)Let X and Y be two discrete random variables with the following joint p.d Y\X 1 2 4 1 0.10 0.15 - 3 0.20 0.30 - 5 0.10 0.15 - Show that E(XY)=E(X)E(Y) [10]
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Q. 4
(a)Let X be random variable with p.d.f. f(x)=2(x−1) 1<x<2 Find the E(2X-1) and E(X²). [10]
(b)Let X and Y have the joint p.d.f described as follows. (x,y) (1,1) (1,2) (1,3) (2,1) (2,2) (2,3) f(x,y) 2/15 4/15 3/15 1/15 1/15 4/15 and f(x,y) is equal to zero elsewhere. Find the two marginal p.d.f 's and the correlation coefficient. [10]
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Q. 5
(a)A certain event is believed to follow the Binomial distribution. In 1024 samples of 5, the result was observed once 405 times and twice 270 times. Find p and q. [10]
(b)A random sampling of 4 members of a 150 members club has shown that 3 prefer no smoking in the clubhouse dining room. What is the probability that this will occur if in fact only 20% of members prefer no smoking in the dining room. Find this probability assuming that the sample was obtained under i) sampling without replacement, and ii)sampling with replacement. Compare the two answers. [10]
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Q. 6
(a)For a normal distribution prove that mean=median=mode=µ. [10]
(b)A random variable X is normally distributed with mean µ=166 and σ = 20 .Find i)P(170<X<200) ii) P(148<X<172) [10]
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Q. 7
(a)If n pairs of values of two variables a and b are given, whereas each variable is ranked in order(1 to n), show that the coefficient of correlation between ranks is given by rs=1−(6∑d2/(n(n2−1)) [6]
(b)Obtain the product moment coefficient of correlation between following values a 7.4 9.0 11.0 2.5 4.6 6.4 b 8.5 6.1 2.4 6.7 12.6 3.3 Rank the values and hence find a rank correlation between the two sets [14]
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Q. 8
(a)Given the following pairs of values of X and Y. X 0 1 2 3 4 Y 10 17 28 43 62 Fit a suitable curve. [10]
(b)The following data represent concomitants values of three variables X 1 X 2 X 3 X 1 32 18 52 16 42 48 X 2 3 2 5 1 4 6 X 3 2 4 2 5 3 9 Calculate all the multiple correlation coefficients. [10]
The 2021 PMS Punjab Statistics paper set by the PPSC. Question wording only; questions marked “Not yet checked” have not been compared with the official paper yet.
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