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Unit 4 - Practice Quiz

CSE273 50 Questions
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1 Which of the following correctly describes a Tensor of rank 0?

A. A Vector
B. A Matrix
C. A Scalar
D. A 3D Array

2 Given two vectors and , what is their dot product ?

A. 7
B. 11
C. [3, 8]
D. 10

3 If matrix has dimensions and matrix has dimensions , what are the dimensions of the product matrix ?

A.
B.
C.
D.

4 Which of the following properties is not necessarily true for matrix multiplication?

A. Associative:
B. Distributive:
C. Commutative:
D. Identity:

5 What is the transpose of the row vector ?

A.
B. A column vector
C. A scalar 6
D. An identity matrix

6 In the equation , what does represent?

A. The Eigenvector
B. The Eigenvalue
C. The Determinant
D. The Gradient

7 Which equation is solved to find the eigenvalues of a square matrix ?

A.
B.
C.
D.

8 If a matrix is a identity matrix, what are its eigenvalues?

A. 0, 0, 0
B. 1, 2, 3
C. 1, 1, 1
D. It has no eigenvalues

9 Geometrically, what happens to an eigenvector when the linear transformation is applied to it?

A. It rotates by 90 degrees.
B. It becomes zero.
C. It gets scaled by a factor of without changing direction (or reversing direction).
D. It becomes orthogonal to the original vector.

10 The sum of the eigenvalues of a matrix is equal to:

A. The determinant of
B. The trace of (sum of diagonal elements)
C. Zero
D. The rank of

11 A variable whose value is subject to variations due to chance is known as:

A. A scalar
B. A Random Variable
C. A constant
D. A derivative

12 Which of the following represents a Discrete Random Variable?

A. The height of a person
B. The temperature outside
C. The number of heads in 10 coin tosses
D. The time taken to run a mile

13 For a probability mass function (PMF) , what is the value of ?

A. 0
B. 0.5
C. 1
D. Undefined

14 The function describing the probability distribution of a continuous random variable is called:

A. Probability Mass Function (PMF)
B. Probability Density Function (PDF)
C. Covariance Matrix
D. Eigenvector

15 What is the expected value (Mean), , of a discrete random variable ?

A.
B.
C.
D. Max()

16 The Variance of a random variable , denoted as , is defined as:

A.
B.
C.
D.

17 If the variance of a dataset is 25, what is the Standard Deviation?

A. 625
B. 5
C. 25
D. 50

18 Which alternative formula is commonly used to calculate Variance?

A.
B.
C.
D.

19 Covariance between two variables and indicates:

A. The exact cause-and-effect relationship.
B. The direction of the linear relationship between variables.
C. The probability of given .
D. The spread of alone.

20 If two random variables and are independent, what is their Covariance?

A. 1
B. -1
C. 0
D. Infinity

21 What is the Joint Probability ?

A. The probability of event X occurring given event Y has occurred.
B. The probability of event X or event Y occurring.
C. The probability that both event X and event Y occur simultaneously.
D. The sum of individual probabilities.

22 Which rule allows us to calculate the Marginal Probability from a joint probability ?

A. Bayes' Theorem
B. Sum Rule (Marginalization)
C. Chain Rule
D. Product Rule

23 How is Conditional Probability defined mathematically?

A.
B.
C.
D.

24 According to the Chain Rule of probability, can be written as:

A.
B.
C.
D.

25 What is the formula for Bayes' Theorem?

A.
B.
C.
D.

26 In Bayes' Theorem , what is called?

A. Posterior
B. Prior
C. Likelihood
D. Evidence

27 In Bayes' Theorem, what is ?

A. Likelihood
B. Posterior
C. Prior
D. Marginal

28 What is the key difference between Likelihood and Probability?

A. They are identical.
B. Probability relates to data given parameters; Likelihood relates to parameters given data.
C. Probability is always greater than Likelihood.
D. Likelihood is for discrete variables only.

29 The goal of Maximum Likelihood Estimation (MLE) is to:

A. Minimize the variance.
B. Find the parameter values that maximize the likelihood of the observed data.
C. Calculate the Bayesian posterior.
D. Integrate the area under the curve.

30 What represents the rate of change of a function with respect to ?

A. Integral
B. Derivative
C. Eigenvalue
D. Determinant

31 What is the derivative of with respect to ?

A.
B.
C.
D.

32 If , what is the partial derivative with respect to ()?

A.
B.
C.
D.

33 The vector containing all first-order partial derivatives of a scalar function is called the:

A. Hessian
B. Gradient
C. Jacobian
D. Laplacian

34 Which rule is used to compute the derivative of a composite function ?

A. Product Rule
B. Quotient Rule
C. Chain Rule
D. Sum Rule

35 Given and , the Chain Rule expresses as:

A.
B.
C.
D.

36 What is the derivative of the natural logarithm function ?

A.
B.
C.
D. 1

37 What is the derivative of the sigmoid function in terms of ?

A.
B.
C.
D.

38 A matrix of second-order partial derivatives is known as the:

A. Gradient
B. Hessian Matrix
C. Jacobian Matrix
D. Identity Matrix

39 If the gradient of a function at a specific point is the zero vector, , that point is a:

A. Global Maximum
B. Stationary Point (Critical Point)
C. Discontinuity
D. Asymptote

40 In Gradient Descent, the update rule for a parameter with learning rate is:

A.
B.
C.
D.

41 What is the derivative of a constant ?

A. C
B. 1
C. 0
D. x

42 For a function , what is ?

A. y
B. x
C. 1
D. 0

43 Which of the following describes a Convex Function?

A. A function with multiple local minima.
B. A function where a line segment between any two points on the graph lies above or on the graph.
C. A function that is never differentiable.
D. A function with a negative second derivative.

44 What is the Jacobian Matrix used for?

A. Representing all second-order derivatives.
B. Representing all first-order partial derivatives of a vector-valued function.
C. Finding the eigenvalues of a scalar.
D. Calculating the variance.

45 If events A and B are mutually exclusive, what is ?

A. 0.5
B. 1
C. 0
D.

46 If and , and A and B are independent, what is ?

A. 0.7
B. 0.1
C. 0.3
D. 0

47 What property of the Normal Distribution makes it symmetric?

A. Mean = Median = Mode
B. Variance = 1
C. It is always positive
D. It has a heavy tail

48 What does the term 'i.i.d' stand for in machine learning and statistics?

A. Integrated Independent Data
B. Independent and Identically Distributed
C. Inverse Identity Distribution
D. Iterative Independent Derivative

49 The derivative of with respect to is:

A.
B.
C.
D.

50 Given a scalar and vector , the product results in:

A. A scalar
B. A vector scaled by
C. A matrix
D. 0
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