Advanced Maths for Data Science Quiz

1.If the value of 'n' is too large,Binomial Distribution ___________.

ans: tends to Poisson Distribution

2.Two random variables are independent if below statements are true:

ans: P(x|y) = P(x), for all values of X and Y.

        P(x∩y) = P(x) * P(y), for all values of X and Y

3. How can yo define the relation between sample size and the standard error of the mean?

ans: standard error decreases as the sample size increases.

4. Bernoulli random variables take (only) the values 1 and 0.

ans: True

5. Find the value of k if f (x, y) = k(1− x)(1− y) for 0 < x, y < 1 is to be joint density function.

ans: 4

6. If a P-value is small enough, then we say the results are statistically significant.

ans: True

7. The expected value of a discrete random variable ‘x’ is given by

ans: ∑ x P(x)

8. Select the correct statements about exponential distribution from the following:

ans: Exponential distribution is bi-variate.

Exponential distribution is only defined for non-negative variables.

9. Point out the correct statement.

ans: The standard error is calculated solely from sample attributes

10. Binomial distribution is negatively skewed when

ans: p>1/2

11. Which of the following represents the fiftieth percentile, or the middle point in a set of numbers arranged in order of magnitude?

ans: Median

12. In the inverse and systems of equations, the matrix inverse for systems of equation is used to determine solution set of equations

ans: True

13. If θ is the angle between two vectors a and b then a.b≥0 only when

ans: 0⩽θ⩽π/2

14. In a criminal trial, a Type I error is made when:

ans: an innocent person is convicted (sent to jail)

15. Which of the following are measures of dispersion?

ans: Standard deviation

        variance

         confidence interval

         inter-quartile range

16. A lottery ticket displays the probabilities of winning various prizes on the back of the ticket. These probabilities are examples of:

ans: Relative frequency probabilities based on physical assumptions.

17. The normal approximation to the binomial distribution is most useful for finding which of the following?

ans: The probability P(X ≤ k) when X is a binomial random variable with large n.

18. The p-value of a test is the:

ans: smallest significance level at which the null hypothesis can be rejected

19. The probability that the confidence interval does contain the parameter is denoted by

ans: 1−α

20. Mean of a constant ‘a’ is.

ans: a

21. Type 1 error occurs when?

ans: We reject Ho if it is True

22. The derivative of cot x is:

ans: -cosec^2 x

23. Consider a dice with the property that that probability of a face with n dots showing up is proportional to n. The probability of face showing 3 dots is?

ans: 3/21

24. What percentage of measurements in a dataset fall above the median?

ans: 0.5

25. A bag has 5 white marbles, 8 red marbles and 4 purple marbles. If we take a marble randomly, then what is the probability of not getting purple marble?

ans: 0.77

26. Samples of size 25 are selected from a population with mean 40 and standard deviation 7.5. The standard error of the sampling distribution of sample means is

ans: 1.5

27. A discrete probability distribution may be represented by-

ans: table

        graph

         Mathematical Equation

28. The determinant of the matrix whose eigen values are 7, 1, 9 is given by

ans:  63

29. Exponential distribution is bi-variate.

ans: False

30. A statement made about a population for testing purpose is called?

ans: Hypothesis

31. Arrange the steps to find eigenvector in the correct order. a.)We find out the covariance matrix of our data set. b.)We find out the Eigenvectors of the covariance matrix. You don’t need to bother much about covariance matrix. It’s an advanced concept of statistics.  As we have data in ‘n’ dimensions, we will find ‘n’ Eigenvectors corresponding to ‘n’ Eigenvalues. c.)We will select ‘k’ Eigenvectors corresponding to the ‘k’ largest Eigenvalues and will form a matrix in which each Eigenvector will constitute a column. We will call this matrix as U. d.)Data is mean normalised and feature scaled.

ans: 4123

32. What function is non-linear?

ans:y=x(2+x)

33.  A range of values within which the population parameter is expected to occur is called:

ans: Confidence interval

34. What values does the describe function give?

ans : mean

         count

          top

          standard deviation

35. Which of the following matrix multiplications would not be possible?

ans:A 5×6 matrix with a 3×3 matrix

36. The values associated with a two-sided 95% confidence interval of the standard normal distribution are

ans: ± 1.96

37. If f (x, y)= kxye^−(x2 + y2 ) , x ≥ , y0 ≥ 0 is the joint pdf, find k .

ans: 4

38. If a matrix A is skew symmetric then, transpose of A is equal to

ans: -A

39. Which of these is a correct alternative hypothesis for a two‐tailed test?

ans: Ha: μ ≠ 7

40.Calculus provides a framework for understanding how mathematical functions behave. Calculus helps us

ans: Understand the steepness at various points on a curve.

       Find the extreme points in a function.

       Determine the optimal function that best represents a dataset.

       Understand the slope and y-intersept at various points on line

41. Which probability distribution is appropriate for a count of events when the events of interest occur randomly, independently of one another and rarely?

ans: poisson distribution

42. The standard normal distribution has a mean of 1 and standard deviation as 0.

ans: False

43. Bernoulli trials are also called as _____ or _____ questions.

ans: yes, no

44. A statement whose validity is tested on the basis of a sample is called?

ans: Statistical Hypothesis

45. Sum of n independent Exponential random variables (λ) results in __________

ans: Gamma random variable

46. Green sea turtles have normally distributed weights, measured in kilograms, with a mean of 134.5 and a variance of 49.0. A particular green sea turtle’s weight has a z-score of -2.4. What is the weight of this green sea turtle? Round to the nearest whole number.

ans: 118 kg

47. In which distribution successive trials are without replacement

ans: Hypergeometric Distribution

48. The concept of eigen values and vectors is applicable on

ans: square matrix

49. If a function is dependent on a number of variables then we can use the partial derivative to find the derivative of the function with respect to one of those variables. We shall keep all of the variables constant.

ans: True

50. Independent random variable doesn’t affect the probability of another event happening

ans: True

51. Which of the following is type of Test Statistics formula

ans:Test Statistic for Proportions

       Test Statistic for Mean

        Test Statistic for Variance

52. The Central Limit Theorem says that the mean of the sampling distribution of the sample means is

ans:  exactly equal to the population mean.

53. With the non-probability sampling methods you do not know the likelihood that any element of a population will be selected in a sample

ans:True

54.Which one of the following is true regarding 'mode' of a sample?

ans:none of the above

55.A parameter is:

ans: a population characteristic

56.A sampling distribution is the probability distribution for which one of the following:

ans:A sample statistic

57.Cumulative distribution functions are used to specify the distribution of multivariate random variables.

ans: True

58. In a two-tail test for the population mean, if the null hypothesis is rejected when the alternative is true, then:

ans:a correct decision is made

59.The test statistic is a value used in making a decision about.

ans:Null Hypothesis

60.The joint p.m.f of (X,Y) is given by P(x, y) = k(2x + 3y), x = 0,1,2 y = 1,2,3.Find the marginal probability distribution of X at x=1.

ans: 24/72

61. Find the mean of tossing 4 coins.

ans: 2

62.  If X and Y are independent RVs with variances 8 and 5.find the variance of 3X+4Y.

ans: 152

63. If the values taken by a random variable are negative, the negative values will have ___________

ans: Positive probability

64.How many independent variables are in a bivariate distribution?

ans: 2

65. Which of the following is an advantage of matrices?

ans: Graph Plotting

66. What is the order of a matrix?

ans:Number of rows X number of columns

67. Which of these distributions is used for a testing hypothesis?

ans:Chi-Squared Distribution

68. For continuous random variables, the CDF is the derivative of the PDF.

ans: False

69. A sample of size 36 is taken from a population with standard deviation 12. The sample mean is found to be 116. In order to construct a confidence interval, one must assume that the population was normally distributed.

ans: False

70. What is the saddle point?

ans:Point where function neither have maximum value nor minimum value

71.If you are throwing two die at same time, they are two independent variables hence the covariance is 0

ans: True

72. The significance level defines how much evidence we require to______.

ans:Reject Null Hypothesis in favor of Alternative Hypothesis

73.Variance of a constant ‘a’ is

ans: 0

74.Let E and F be events of a sample space S of an experiment, if P(S|F) = P(F|F) then value of P(S|F) is __________

ans: 1

75. When you multiply a matrix by the identity matrix, you obtain the Inverse matrix.

ans: False

76. If the outcomes of a discrete random variable follow a Poisson distribution, then their

ans: Mean equals the Variance

77. A professor asked students in a class their ages. On the basis of this information, the professor states that the average age of all the students in the university is 22.5 years. This is an example of

ans:statistical inference

78.If two events (both with probability greater than 0) are mutually exclusive, then:

ans:They cannot be independent.

79.Normal Distribution is applied for ___________

ans:Continuous Random Distribution

80.What will be the confidence level if the level of significance is 5% (0.05)?

ans: 0.95

81. Which function is used to give summary of the dataframe

ans: describe

82.Which of the following factors do not affect the width of the confidence interval?

ans: Sample mean

83.Mode is the value of x where f(x) is a maximum if X is continuous.

ans: True

84. Which of the following is true regarding Determinant of a Matrix?

ans: The concept of determinant is applicable to square matrices only.

85. The jacobian of p,q,r w.r.t x,y,z given p=x+y+z, q=y+z, r=z is ________

ans: 1

86. A is a unitary matrix. Then eigen value of A are

ans: i, -i 

87.On which of the following does the critical value for a chi-square statistic rely?

ans: The degrees of freedom

88.Which one of these is not one of the conditions for the binomial distribution?

ans: Trials must be more than 4  

89. Given E(X) = 12 and E(Y) = -5, then E(X – Y) is

ans: 17

90. Bernoulli trials only deal with mutually exclusive outcomes.

ans: True

91. Which of the following statements best describes the relationship between a parameter and a statistic?

ans: A statistic is used to estimate a parameter.

92.The covariance is: (Multiple select)

ans: A measure of the strength of relationship between two variables.

       Dependent on the units of measurement of the variables.

        An unstandardized version of the correlation coefficient. 

93.If f(x) is a probability density function of a continuous random variable, then lim-∞ to ∞ ∫f(x)=?

ans: 1

94.Two distributions are independent if the joint distribution is the same as the product of the two marginal distributions.

ans: True

95.When do the conditional density functions get converted into the marginally density functions?

ans:   Only if random variables exhibit statistical independency

96. Which of the following property does hold for matrix multiplication?

ans: Associative

        Distributive

        Additive Inverse 

97. Exponential distribution is a special case of gamma distribution.

ans: True

98. For a given standard error, lower confidence levels produce wider confidence intervals.

ans: False

99. Find the slope of x^2.y = 8 at the point (2, 2)

ans: -2

100. For n x n matrices A and B, is (AB)^ 2 = A^2B^2 ?

ans: False