GTU 3130006 Probability and Statistics (PS) Winter 2024 Question Paper & PDF

One card is drawn at random from a pack of 52 cards. Find the probability of getting a king or a red card.

Data on the readership of a certain magazine show that the proportion of male readers under 35 is 0.40 and that over 35 is 0.20. If the proportion of readers under 35 is 0.70, find the probability of subscribers that are female over 35 years. Also, calculate the probability that a randomly selected male subscriber is under 35 years of age.

Three students 𝐴, 𝐵, 𝐶 are in a running race. If 𝑃(𝐴) = 𝑃(𝐵) = 2𝑃(𝐶), then find the probability that 𝐵 or𝐶 wins.

Let X be a continuous random variable with pdf 𝑓(𝑥) = 𝑘𝑥(1 − 𝑥), 0 ≤ 𝑥 ≤ 1 Find 𝑘 and determine 𝑃(0 ≤ 𝑋 ≤ 0.5).

1 white, 2 red, and 3 black balls 2 white, 3 red and 1 black ball, and 3 white, 1 red and 2 black balls. One urn is chosen at random and two balls are drawn. They happen to be white and red. Find the probability that they came from (i) Urn 𝐼

Let the continuous random variable X have the probability density function 𝑓(𝑥) = { 1 𝑥4 ; 1 < 𝑥 < ∞ 0; 𝑜𝑡ℎ𝑒𝑤𝑖𝑠𝑒 Find distribution function 𝐹(𝑥).

𝑋 −3 −2 −1 0 1 2 𝑃(𝑋 = 𝑥) 0.05 0.1 0.2 0.3 0.2 0.15 Find (i) 𝐸(𝑋) (ii)𝑉𝑎𝑟(𝑋).

Compute Karl Pearson’s coefficient of correlation between 𝑋 and 𝑌 for the following data: 𝑥 2 4 5 6 8 11 𝑦 18

Explain the term related to testing of hypothesis: (i) One Tailed Test

A coinwas tossed 960 times and returned heads 183 times. Test the hypothesis that the coin is unbiased.Usea 0.05 level of significance? (|𝑍0.05| = 1.96)

In a city A, 20% of a random sample of 900 school boys has a certain slight physical defect. In another city B, 18.5% of a random sample of 1600 school boys has the same defect. Is a difference between the proportions significant at 0.05 level of significance? (|𝑍0.05| = 1.96)

Using least squares approximation method, fit a straight line𝑦 = 𝑎𝑥 + 𝑏 to the following data: 𝑥 1 2 3 4 5 𝑦 14 27 40 55 68

Using least squares approximation method,fit a curve 𝑦 = 𝑎𝑒𝑏𝑥 to the following data: 𝑥 1 5 7 9 12 𝑦 10 15 12 15 21

Distribution of height of 1000 students is normal with mean 165 cms and standard deviation 15 cms. How many soldiers are of height (i) less than 138 cms. (ii) more than 198 cms. (iii) between 138 and 198 cms. (𝑃(𝑧 = 1.8) = 0.4641, 𝑃(𝑧 = 2.2) = 0.4841)