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WorksheetsStatistics and Probability Quiz
Total questions: 25
Worksheet time: 13mins
Given a dataset, calculate the variance of the numbers: [2, 4, 6, 8, 10].
4
6
8
10
The eigenvalues of a 4x4 square matrix having 0's as the diagonal elements and 1's on the off diagonal elements is:
2, -2, 0, 0
1, -1, 1, -1
3, -1, -1, -1
4, 0, 0, 0
You pick a coin at random from a bag containing a fair coin and a two-headed coin. You flip the coin twice and get heads both times. What is the probability that you picked the fair coin?
1/3
4/13
1/5
2/5
In medical screening, it is sometimes more important to avoid false negatives than false positives. How would this affect the p-value we might use for a medical test?
we would choose a higher p-value
we would choose a lower p-value
we would choose the same p-value
false negatives do not depend on p-value
Given y=x^x, what is dy/dx at x = 2?
4(1+log2)
4(2+log2)
4
8
In a scenario where you need to group customers based on purchasing behavior without prior labels, which algorithm should you use?
Linear regression
K-means clustering
Logistic regression
Random forest
For random variables X and Y, we have Var(X)=1, Var(Y)=4, and Var(2X-3Y)=34, then the correlation between X and Y is:
1/2
1/4
1/3
None of the above
Two squares are chosen at random on a chessboard. What is the probability that they have a side in common?
8/13
17/18
5/13
1/18
Suppose you have a dataset with m=50 examples and n=200000 features for each example. You want to use multivariate linear regression to fit the parameters Θ. Should you prefer gradient descent or the normal equation?
Gradient descent, since inverse(X^T X) will be very slow to compute
Gradient descent, since it will always converge to the optimal Θ
The normal equation, since it provides an efficient way to directly find the solution
The normal equation, since gradient descent might be unable to find the optimal Θ
Let M and S² be the mean and variance of a random sample of size > 1 from a normal population with unknown mean μ and unknown finite variance σ²>0. Which statements are true?
((n-1)/n)M is an unbiased estimator of μ, and ((n-1)/n)S² is an unbiased estimator of σ²
1 only
S² is an unbiased estimator of σ², and S is an unbiased estimator of σ
Both 1 and 2
2 only
Given a graph of a model's training and validation error, determine if it represents underfitting or overfitting.
Underfitting
Overfitting
Neither
Both
You have two coins. One is fair (1/2 heads probability) and the other is biased (3/4 heads probability). You randomly pick a coin and flip it twice, getting heads both times. What is the probability that you picked the fair coin?
13/32
4/13
2/13
19/32
If rank(A) is 2 and rank(AB) is 3, then:
rank(B) = 3
rank(B) <= 3
rank(B) >= 3
data insufficient
The number of solutions for the system: 2x+y-z=4, x-2y+z=-2, -x+2y-z=-2 is:
0
1
Inf
Can't be determined
When classifying data with logistic classification, what is the upper bound of the likelihood in the maximum likelihood method? Is this value attainable?
1, Yes
e, No
1, No
0, Yes
A 3-input neuron has weights 1, 4 and 3. The transfer function is linear with constant of proportionality = 3. The inputs are 4, 8 and 5 respectively. What will be the output?
51
153
54
160
Which statements about PCA are correct?
(i), (ii) and (iv)
(ii) and (iv)
(iii) and (iv)
(i) and (iii)
Given a scenario involving a dataset with labeled data and a need to predict a continuous output, which algorithm is most suitable?
K-means clustering
Linear regression
Decision tree classifier
Support vector machine (SVM) with RBF kernel
The system x + y + z = 1, ax - ay + 3z = 5, 5x - 3y + az = 6 has infinite solutions if a =?
-3
3
-4
4
Police enforce speed limits on routes A, B, C, D operated 40%, 30%, 20%, 30% of time. Biff speeds with route probabilities 0.2, 0.1, 0.5, 0.2. What's the probability he gets a ticket?
0.27
0.93
0.73
0.07
Let A be a 2×2 matrix with a11=a12=a21=+1 and a22=-1. The eigenvalues of matrix A^19 are:
1024 and -1024
1024√2 and -1024√2
4√2 and -4√2
512√2 and -512√2
If the characteristic equation of matrix A is t²-t-1=0, then:
A^(-1) does not exist
A^(-1) exists but cannot be determined
A^(-1) = A - I
A^(-1) = A + I
Fitting data from a cubic function corrupted by Gaussian noise using linear (M1) and 5th degree polynomial (M5) models:
Bias(M1) ≤ Bias(M5), Variance(M1) ≤ Variance(M5)
Bias(M1) ≥ Bias(M5), Variance(M1) ≤ Variance(M5)
Bias(M1) ≤ Bias(M5), Variance(M1) ≥ Variance(M5)
Bias(M1) ≥ Bias(M5), Variance(M1) ≥ Variance(M5)
Two squares are chosen at random on a chessboard. What is the probability that they have a side in common?
1/36
1/9
2/9
1/18
The system 2x+y-z=1, x-2y+z=-2, -x+2y-z=-1 has how many solutions?
0
1
2
Infinitely many
