GTU 3130006 Probability and Statistics (PS) Winter 2025 Question Paper & PDF

A can 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.

Three companies A, B and C supply 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?

A random variable X has the following probability function X=x -2 -1 0 1 2 3 P(X=x) 0.1 K 0.2 2K 0.3 3K

Four balls are drawn simultaneously from a bag containing 6 white, 5 black and 7 red balls. Find E(X), where X denotes number of white drawn.

It is known that the mean diameters of rivets produced by two firms A and B are 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 A have the same variability as those of firm B. Using the value F0.05 (15,21) = 2.20

Fit a curve of the formx ab y = to the following data x : 1 2 3 4 5 6 7 y : 87 97 113 129 202 195 193

Find the mean and median for the given data

The first four moments of a distribution about the value 5 of the variate are 2, 20, 40, and 50. Find mean and variance.

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

A speaks truth in 75% cases and B in 80% cases. Find the probability that they are likely to contradict each other in stating the same fact.

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 4 or more will suffer from disease?

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.

A sample 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)

Below are given the gain in weights (in lbs) of pigs fed on two diets A and 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 t0.05 at 25 d. f. = 2.07)

From the following table, test the hypothesis that the flower colour is independent of flatness of leaf Flat leaves Curled leaves Total White flowers 99 36 135 Red flowers 20 5 25 Total 119 41 160 If the value of2  for 1 d. f at 5% level of significance is 3.841.