TBSE Class 12 Model Question Paper 2021 Statistics

MODEL QUESTION Class - XII : Statistics : Time -3h 15m : Marks- 80 : 2020-2021 Group -A : Each Question Carries 1 Mark : 1x20=20 1) What is measured by correlation coefficient ? 2) What is random variable ? 3) Give the interpretation of cov (x,y). 4) if Xxy=0, then X and Y are _____ if X and Y takes two values 0,1 with positive probalities. 5) Give the limits of correlation coefficient. 6) if X is a random variable and f(x) is an increasing function, than f(x) is a _____. 7) What is sample space ? 8) Write the Pmf of poisson distribution. 9) Write the number of parameters of a Binomial distribution. 10) Who discovered poisson distribution? 11) What is rank correlation ? 12) Is it true that a correlation coefficient of γ =0.8 indicate a relationship twice as close as γ =0.4? 13) What is unbaised statistic ? 14) if γ =0.5 then can we say that 50% of the data are explained ? 15) What is random experiment ? 16) Going to moon and then finding out if there is life. Is it a randon experiment ? 17) What is the coefficient of rank correlation if ranks of X and Y are the same ? 18) Define mutually exclusive events. 19) What is the probability of an impossible event ? 20) What is the probability of a sure event ? Group - B : Each Question Carries 2 Marks : 2x5=10 21) For any two random variable X and Y. Cov (X,Y)=3, Find the value of Cov (5x+4, Y) 22) Write down two characteristics of the Normal distribution. 23) If X is a random variable then show that v(ax+b) = a2v(x) 24) Find the mean of a poisson distribution with parameter. 25. Show that the degree of linear asociationship between two variables cannot exceed +1. Group-C : Each Question Carries 3 3x5=15 26. If v(x)=9, v(y) 4 and v(x–y)=v(x), find the correlation coefficient between x and y. 27. An urn contains 4 tickets numbered 1,2,3,4 and another contains 6 ticket numbered 2,4,6,7,8,9. If one of the two urns is chosen at random and a ticket is drawn at random from the chosen urn find the probabilities that the ticket drawn bears the number 2 or 4. 28. State and prove Bayes theorem. 3 5 3 5 29. If A and B be two events such that P(A) = and P (B) = show that ≤ P(A ∩ B) ≤ . 4 8 8 8 30. T is an unbaised estimator of θ show that T is a baised estimator of θ

Group-D : Each Questions Carries 5 Marks : 5x5=25 x−2 1 3 31. Show that dx = log ( x − 1) + log ( x − y ) + c ( x − 1)( x − 5) 4 4 32. Obtain the angle between two regression lines. 33. Obtain the median of Normal distribution with parameter µ and δ 2 . 34. For any two events A and B show that P ( A ∩ B ) ≤ P ( A) ≤ P ( A ∪ B ) ≤ P ( A) + P ( B ) 2+4 35. X1, X2 and X3 are a random sample of size 3 from a population with mean µ and variance δ 2 . T1, T2, T3 are the three estimators used to estimate mean vaule µ where, 1 T1 = x1+x2–x3, T2=2x1+3x3–4x2, T3 = ( x +x +x ) 3 λ 1 2 3 i) Are T1 and T2 unbaised estimators ? ii) Find the value of λ such that T3 is unbaised estimator for µ . 2+3