Define independent events and provide an example
[3 marks]Acoin is tossed three times. What is the probability of getting exactly two heads?
[4 marks]Find the best fitting parabola: x 1 2 3 4 y 2 5 10 17 26
[5 marks]Does there exists a binomial distribution for which variance is greater than mean?
[3 marks]Abiased coin returns head 10% of times. Find the probability of getting exactly 2 heads in 10 trials using binomial distribution.
[4 marks]Afactory has three machines A, B, and Cproducing 20%, 30%, and 50% of the total items, respectively. The probabilities of producing a defective item are 1%, 2%, and 3% for A, B, and C, respectively. If an item is defective, what is the probability that it was produced by machine B?
[7 marks]Afactory produces light-bulbs. The probability of a bulb being defective is 0.02. If 200 bulbs are tested, use the Poisson approximation to find the probability that at least three bulbs are defective.
[7 marks]Find the mean and median of 2, 3, 5,
[3 marks]Calculate the rank correlation: x 1 2 3 4 y 2 1 5 4
[3 marks]Find the correlation coefficient. x 1 2 3 4 5 6 y 6 8 11 9 12 10
[14 marks]Find mode x 0-10 10-20 20-30 30-40 y 10 20 40 30
[3 marks]Calculate first four central moments of observations 3,5,7,13
[4 marks]Find regression line of Yon X x 2 4 6 8 y 5 12 19 26 33
[10 marks]Explain the terms one-tailed and two-tailed test
[3 marks]In a sample of 500 bulbs 20 are found defective. The company claims that only 2% bulbs are defective. Test the reality of claim at 5% level of significance.1
[4 marks]Test whether the following samples could have been drawn from population with same SD. Sample A Sample B Size 100 200 SD 10 11
[7 marks]Explain the terms null and alternate hypothesis
[3 marks]Acoin returned 531 heads in 1000 tosses. Is it biased? [Use 𝛼 = 0.05]
[4 marks]Use chi-square test to determine whether smoking and hypertension are independent at 5% level of significance[𝜒2(𝛼 = 0.05,df = 1) = 3.84] Smoking No Smoking Hypertension 30 No Hypertension 10 40
[20 marks]State Chebyshev’s inequality.
[3 marks]Two cards are chosen randomly from deck. What is probability that (a) both are ace? (b) both are black? (c) none is ace (d) none is black
[4 marks]Weight of 1000 experimental animals is normally distributed with mean 235 grams and standard deviation 35. How many animals weigh (a) below 172 grams (b) above 312 grams (c) between 172 to 312 grams. [P(Z=1.8)=0.4641,P(Z=2.2)=0.4841]
[7 marks]If Aand Bare independent events with P(A)=0.5, P(B)=0.4 then find P(AᴜB)
[3 marks]Find the best fitting line to the points (1,1), (2,4), (3,9), (4,16)
[4 marks]Fit the curve y = abx x 1 2 3 y 35 70 140 280
[4 marks]