PSC HSST Statistics Model Questions and Answers

26. Which one among the following is the first of the major Environmental Protection Act promulgated in India?
(A) Water Act
(B) Air Act
(C) Forest Conservation Act
(D) Noise Pollution Rule
Answer: A

27. In order to be eligible for gratuity under the Payment of Gratuity Act, 1972, an employee should have a minimum continuous service of:
(A) 10 years
(B) 5 years
(C) 7 years
(D) 3 years
Answer: B

28. Under the provisions of prevention of sexual harassment (at work place) Act, the term aggrieved woman means:
(A) a woman employee belong to govt. sector
(B) a woman employee belong to private sector
(C) a domestic worker
(D) all of the above
Answer: D

29. According to Right to Information Act, within what time should the information be provided to an applicant in normal cases:
(A) 45 days
(B) 90 days
(C) 60 days
(D) 30 days
Answer: D

30. Who is an adolescent as per Factories Act 1948?
(A) who has completed 17 years of age
(B) who is less than 18 years
(C) who has completed 15 years but less than 18 years
(D) none of the above
Answer: C

31. If `A_n={(A if n “is odd”),(B if n “is even”):}`
then lim inf `A_n=“ `
(A) `AuuB`
(B) `quadAnnB`
(C) `quadA` Δ`quadB`
(D) `phi`
Answer: B

32. Which of the following statement(s) is/are wrong?
I: A monotone field in not a sigma field
II: A sigma field is a monotone field
(A) I alone
(B) II alone
(C) Neither I nor II
(D) Both I and II
Answer: A

33. If `quadmu_1` is a measure defined on a sigma field `quadfrA_1` and `quadmu_2` is a measure defined on a sigma field `quadfrA_2` , then `quadmu_1+mu_2` is a measure only when
(A) `quadfrA_1subfrA_2`
(B) `quadfrA_1supfrA_2`
(C) `quadfrA_1=frA_2`
(D) `quadfrA_1!=frA_2`
Answer: C

34. Which of the following statement(s) is/are true?
A : Every subsets of are Borel sets
B : Every Borel set in measurable
(A) A alone
(B) B alone
(C) Neither A nor B
(D) Both A and B
Answer: B

35. Let `quadI = (0, 1)` , be the Borel field of subsets of `quadI` and `mu` is the Lebesgue measure on. For `quadn = 1, 2,….,` if `quadA_n=(0,1/n), mu(lim “sup” A_n)=`
(A) 0
(B) 0.5
(C) 1
(D) `1/n`
Answer: A

36. Let `quadW` be the subspace of generated by the vectors (1, -2, 5, -3), (2, 3, 1, -4) and (3, 8, -3, -5). Then the dimension of `quadW` is
(A) 4
(B) 3
(C) 2
(D) 1
Answer: C

37. For any arbitrary matrices `quadA` and `quadB` , the sum of ranks of `quadA` and `quadB` is always
(A) less than rank `quad(A+B)`
(B) less than or equal to rank`quad(A+B)`
(C) greater than rank`quad(A+B)`
(D) greater than or equal to rank`quad(A+B)`
Answer: D

38. Let `quadA` and `quadB` are `quadnxxn` square matrices. Then the eigen values of `quadAB` are same as the eigen values of
(A) `quadA+B`
(B) `quadA-B`
(C) `quadB-A`
(D) `quadBA`
Answer: D

39. The quadratic polynomial corresponds to the matrix `quadA=((1,0,1/2),(0,0,-1),(1/2,-1,0))` ` ` is
(A) `quadx^2+1/2xz-xy`
(B) `quadx^2-2yz+xz`
(C) `quadx^2+1/2yz-xy`
(D) `quadx^2+yz-2xz`
Answer: B

40. Let `quadP` be an `quadmxxm` orthogonal matrix, `quadQ` be an `quadnxxn` orthogonal matrix and `quadA` any `quadmxxn` matrix. If `quadA^T` denote the transpose of `quadA` and `quadA^-` denote the generalized inverse of `A` , then the generalized inverse of `quadPAQ` is
(A) `quadP^TA^{-}Q^T`
(B) `quadQ^TA^{-}P^T`
(C) `quadPA^{-}Q`
(D) `quadQA^{-}P`
Answer: B

41. If `quad{A_n}` is a sequence of events on a probability space (Ω,`quadA,P)` such that `quadA_n->A` as `quadn->oo` , then what is the value of lim`quadP(A_n)` ?
(A) zero
(B) one
(C) `quadP(A)`
(D) need not exist
Answer: C

42. If `quadA` and `quadB` are mutually exclusive events, each with positive probabilities, then they are
(A) independent events
(B) dependent events
(C) equally likely events
(D) exhaustive events
Answer: B

43. If `quad{A_n}` is a sequence of events such that `quadsum_(k=1)^ooP(A_k)=oo` , then `quadP(lim”sup”A_n)=1` provided events are
(A) equally likely
(B) Mutually exclusive
(C) independent
(D) pair-wise mutually exclusive
Answer: C

44. Let `quad{A_n}` be a sequence of events such that `quadB_1=A_1` and `quadB_k=A^c_1 A^c_2…` `A_{k-1}^c A_k` for `quadk>=2` , in which `quadA^c` is the complement of `quadA` . Then the sequence of events `quad{B_n}` are
(A) Pair-wise independent
(B) Mutually independent
(C) Mutually dependent
(D) Pair-wise mutually exclusive
Answer: D

45. If `quadX` is a random variable with finite expectation, then the value of `quadxP(X<-x)` as `quadx->oo` is
(A) infinity
(B) unity
(C) zero
(D) indeterminate
Answer: C

46. If `quadX` is a symmetric random variable with distribution function `quadF` and real valued characteristic function Φ, then for any `quadx` in ,`quadF(x)=`
(A) `quadF(-x)`
(B) `quadF(-x-0)`
(C) `quadF(-x-0)-1`
(D) `quad1-F(-x-0)`
Answer: D

47. If the characteristic function Φ of distribution function `quadF` is absolutely integrable on , then for any`quadx` in , `quad f’={dF(x)}/dx` is
(A) bounded
(B) uniformly continuous
(C) both (A) and (B)
(D) Neither (A) nor (B)
Answer: C

48. Let `quadX` and `quadX_n` be independent standard normal variables on a probability space (Ω,`quadfrA,P)` ` `, for `quadn>=1` . Then which of the following is not true?
(A) `X_nstackrel(P)(->)X`
(B) `X_nstackrel(d)(->)X`
(C) `quadE(X_n-X)=0`
(D) `quadVar(X_n-X)=2`
Answer: A

49. The sequence `quad{X_n}` of independent random variables, each with finite second moment, obeys SLLN if
(A) `quadsum_(k=1)^ooVar(X_k)<oo`
(B) `quadsum_(k=1)^oo{Var(X_k)}/k<oo`
(C) `quadsum_(k=1)^oo{Var(X_k)}/sqrt(k)<oo`
(D) `quadsum_(k=1)^oo{Var(X_k)}/k^2<oo`
Answer: D

50. Let `quad{X_n}` sequence of independent random variables with
`quadP(X_k=+-k)=1/2k^-Lambda` and `quadP(X_k=0)=1-k^-Lambda` , for `quadk>=1`
Then the sequence does not obey CLT if
(A) `quadLambda=0`
(B) `quadLambda=1`
(C) `quadLambdain(0,1/2)`
(D) `quadLambdain(1/2,1)`
Answer: B