Recent questions tagged statistics / GATE Overflow for GATE CSE

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Memory Based GATE DA 2024 | Question: 41
Consider two random variables, $x$ and $y$, defined as follows: \[ x = \begin{cases} 1 & \text{if HH } \\ 0 & \text{otherwise} \end{cases} \] \[ y = \begin{cases} 1 & \text{if at least one head} \\ 0 & \text{otherwise} \end{cases} \] What is the covariance between $x$ and $y?$

Consider two random variables, $x$ and $y$, defined as follows:\[x =\begin{cases}1 & \text{if HH } \\0 & \text{otherwise}\end{cases}\]\[y =\begin{cases}1 & \text{if at le...

GO Classes

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GO Classes asked Feb 4

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Neural Network | ML | DA Practice
You have a single hidden-layer neural network for a binary classification task. The input is $X \in \mathbb{R}^{n \times m}$, output $\hat{y} \in \mathbb{R}^{1 \times m}$, and true label $y \in \mathbb{R}^{1 \times m}$. The forward propagation equations are: ... $\frac{\partial J}{\partial W^{[1]}} = (\hat{y} - y) \cdot \sigma'(z^{[1]}) \cdot X^T$

You have a single hidden-layer neural network for a binary classification task. The input is $X \in \mathbb{R}^{n \times m}$, output \(\hat{y} \in \mathbb{R}^{1 \times ...

rajveer43

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rajveer43 asked Jan 27

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ML | DA Practice Questions
What is Error Analysis? (i) The process of analyzing the performance of a model through metrics such as precision, recall or F1-score. (ii) The process of scanning mis-classified examples to identify weaknesses of a model. (iii) The process ... to reduce the loss function during training. (iv) The process of identifying which parts of your model contributed to the error.

What is Error Analysis?(i) The process of analyzing the performance of a model through metrics such as precision, recall or F1-score.(ii) The process of scanning mis-clas...

rajveer43

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rajveer43 asked Jan 27

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AI Sample Question for DS-AI
Imagine you are guiding a robot through a grid-based maze using the A* algorithm. The robot is currently at node A (start) and wants to reach node B (goal). The heuristic function $h(n)$ is the Euclidean distance between a node and the goal. The ... algorithm explore next based on the A* calculation? A) Node C B) Node D C) Node E D) Not enough information to decide

Imagine you are guiding a robot through a grid-based maze using the A* algorithm. The robot is currently at node A (start) and wants to reach node B (goal). The heuristi...

rajveer43

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rajveer43 asked Jan 16

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5

UPENN | DS-AI Sample | Decision Tree
When choosing one feature from $X_1, \ldots, X_n$ while building a Decision Tree, which of the following criteria is the most appropriate to maximize? (Here, $H()$ means entropy, and $P()$ means probability) (a) $P(Y | X_j)$ (b) $P(Y) - P(Y | X_j)$ (c) $H(Y) - H(Y | X_j)$ (d) $H(Y | X_j)$ (e) $H(Y) - P(Y)$

When choosing one feature from $X_1, \ldots, X_n$ while building a Decision Tree, which of the following criteria is the most appropriate to maximize? (Here, $H()$ me...

rajveer43

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rajveer43 asked Jan 16

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UPENN | ML | DECISION TREE
Given the following table of observations, calculate the information gain $IG(Y |X)$ that would result from learning the value of $X$. X Y Red True Green False Brown False Brown False (a) 1/2 (b) 1 (c) 3/2 (d) 2 (e) none of the above

Given the following table of observations, calculate the information gain $IG(Y |X)$ that would result from learning the value of $X$. XYRedTrueGreenFalseBrownFalseBrownF...

rajveer43

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rajveer43 asked Jan 16

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7

UPENN | ML Questions for GATE DA
In fitting some data using radial basis functions with kernel width $σ$, we compute training error of $345$ and a testing error of $390$. (a) increasing $σ$ will most likely reduce test set error (b) decreasing $σ$ will most likely reduce test set error (C) not enough information is provided to determine how $σ$ should be changed

In fitting some data using radial basis functions with kernel width $σ$, we compute training error of $345$ and a testing error of $390$.(a) increasing $σ$ will most li...

rajveer43

268 views

rajveer43 asked Jan 15

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DA Practice | UPENN | ML | Naive Bais
Suppose you have a three-class problem where class label $ y \in \{0, 1, 2\} $, and each training example $ \mathbf{X} $ has 3 binary attributes $ X_1, X_2, X_3 \in \{0, 1\} $. How many parameters do you need to know to classify an example using the Naive Bayes classifier? (a) 5 b) 9 (c) 11 (d) 13 (e) 23

Suppose you have a three-class problem where class label $ y \in \{0, 1, 2\} $, and each training example $ \mathbf{X} $ has 3 binary attributes \( X_1, X_2, X_3 \in ...

rajveer43

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rajveer43 asked Jan 14

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2 answers

9

UPENN | ML | Cross validation
Suppose you have picked the parameter $ \theta $ for a model using 10-fold cross-validation. The best way to pick a final model to use and estimate its error is to (a) pick any of the 10 models you built for your model; use its error estimate on ... a new model on the full data set, using the $ \theta $ you found; use the average CV error as its error estimate

Suppose you have picked the parameter $ \theta $ for a model using 10-fold cross-validation. The best way to pick a final model to use and estimate its error is to(a) p...

rajveer43

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rajveer43 asked Jan 13

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1 answer

10

UPENN | ML | Cross Validation
P1: In the limit of infinite training and test data, consistent estimators always give at least as low a test error as biased estimators. P2: Leave-one out cross validation (LOOCV) generally gives less accurate estimates of true test error than 10-fold ... following Statements is/are correct? Only P1 is True Only P2 is True P1 is True and P2 is False Both are False

P1: In the limit of infinite training and test data, consistent estimators always give at least as low a test error as biased estimators. P2: Leave-one out cross validati...

rajveer43

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rajveer43 asked Jan 13

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11

UPENN | ML | DA Practice | Regularization
After applying a regularization penalty in linear regression, you find that some of the coefficients of $w$ are zeroed out. Which of the following penalties might have been used? (a) L0 norm (b) L1 norm (c) L2 norm (d) either (A) or (B) (e) any of the above

After applying a regularization penalty in linear regression, you find that some of the coefficients of $w$ are zeroed out. Which of the following penalties might have be...

rajveer43

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rajveer43 asked Jan 13

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UPENN | ML | DA Practice
Using the same data as above $ \mathbf{X} = [-3, 5, 4] $ and $ \mathbf{Y} = [-10, 20, 20] $, assuming a ridge penalty $ \lambda = 50 $, what ratio versus the MLE estimate $ \hat{\mathbf{w}}_{\text{MLE}} $ do you think the ridge regression $ L_2 $ estimate $ \hat{\mathbf{w}}_{\text{ridge}} $ will be? (a)] 2 b)] 1 (c)] 0.666 (d)] 0.5

Using the same data as above $ \mathbf{X} = [-3, 5, 4] $ and $ \mathbf{Y} = [-10, 20, 20] $, assuming a ridge penalty $ \lambda = 50 $, what ratio versus the MLE es...

rajveer43

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rajveer43 asked Jan 13

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13

UPENN | ML | DA Practice
Consider the statements: $P1:$ It is generally more important to use consistent estimators when one has smaller numbers of training examples. $P2:$ It is generally more important to used unbiased estimators when one has smaller numbers of training examples. Which of the following statement( ... $P1$ and $P2$ are true (C) Only $P2$ is True (D) Both $P1$ and $P2$ are False

Consider the statements:$P1:$ It is generally more important to use consistent estimators when one has smaller numbers of training examples.$P2:$ It is generally more imp...

rajveer43

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rajveer43 asked Jan 13

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1 answer

14

DA Practice | UPENN | ML | Bias-Variance Trade Off | Regularization
Suppose we have a regularized linear regression model: \[ \text{argmin}_{\mathbf{w}} \left||\mathbf{Y} - \mathbf{Xw} \right||^2 + k \|\mathbf{w}\|_p^p. \] What is the effect of increasing \( p ... , decreases variance (c)] Decreases bias, increases variance (d)] Decreases bias, decreases variance (e)] Not enough information to tell

Suppose we have a regularized linear regression model: \[ \text{argmin}_{\mathbf{w}} \left||\mathbf{Y} - \mathbf{Xw} \right||^2 + k \|\mathbf{w}\|_p^p. \] What is the eff...

rajveer43

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rajveer43 asked Jan 13

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15

UPENN | ML | DA Practice | Bias-Variance Trade-Off
Suppose we have a regularized linear regression model: \[ \text{argmin}_{\mathbf{w}} \left||\mathbf{Y} - \mathbf{Xw} \right||^2 + \lambda \|\mathbf{w}\|_1. \] What is the effect of increasing $ \lambda $ ... bias, decreases variance (c)] Decreases bias, increases variance (d)] Decreases bias, decreases variance (e)] Not enough information to tell

Suppose we have a regularized linear regression model: \[ \text{argmin}_{\mathbf{w}} \left||\mathbf{Y} - \mathbf{Xw} \right||^2 + \lambda \|\mathbf{w}\|_1. \] What is the...

rajveer43

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rajveer43 asked Jan 13

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1 answer

16

GATE 2016 | MATHS | Q-33
Suppose $ X $ and $ Y $ are two random variables such that $ aX + bY $ is a normal random variable for all $ a, b $ in $ \mathbf{R} $. Consider the following statements P, Q, R, and S: (P) : $ X $ is a standard normal random variable. (Q) ... 0. Which of the above statements ALWAYS hold TRUE? (A) both P and Q (B) both Q and R (C) both Q and S (D) both P and S

Suppose $ X $ and $ Y $ are two random variables such that $ aX + bY $ is a normal random variable for all $ a, b $ in $ \mathbf{R} $. Consider the following st...

rajveer43

120 views

rajveer43 asked Jan 11

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17

GATE 2018 | MATH | Q-64
Let $X_1$ and $X_2$ be independent geometric random variables with the same probability mass function given by $P(X = k) = p(1 - p)^{k-1}$, $k = 1, 2, \ldots$. Then the value of $P(X_1 = 2 | X_1 + X_2 = 4)$ correct up to three decimal places is____________

Let $X_1$ and $X_2$ be independent geometric random variables with the same probability mass function given by $P(X = k) = p(1 - p)^{k-1}$, $k = 1, 2, \ldots$. Th...

rajveer43

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rajveer43 asked Jan 11

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1 answer

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GATE 2018 | MATHS | Q-62
Let $X1, X2, X3, X4$ be independent exponential random variables with mean $1, 1/2, 1/3, 1/4,$ respectively. Then $Y = min(X1, X2, X3, X4)$ has exponential distribution with mean equal to

Let $X1, X2, X3, X4$ be independent exponential random variables with mean $1, 1/2, 1/3, 1/4,$ respectively. Then $Y = min(X1, X2, X3, X4)$ has exponential distribution w...

rajveer43

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rajveer43 asked Jan 11

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GATE 2018 | MATHS | QI47
Let $\{X_i\}$ be a sequence of independent Poisson($\lambda$) variables, and let $W_n = \frac{1}{n} \sum_{i=1}^{n} X_i$. Then the limiting distribution of $\sqrt{n}(W_n - \lambda)$ is the normal distribution with zero mean and variance given by (A) $1$ (B) $\sqrt{\lambda}$ (C) $\lambda$ (D) $\frac{\lambda}{2}$

Let $\{X_i\}$ be a sequence of independent Poisson($\lambda$) variables, and let $W_n = \frac{1}{n} \sum_{i=1}^{n} X_i$. Then the limiting distribution of \(\sqrt{n...

rajveer43

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rajveer43 asked Jan 11

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20

GATE DA Paper | Practice Problems
Let $𝑌_1 < 𝑌_2 < ⋯ < 𝑌_n$ be the order statistics of a random sample of size $𝑛$ from a continuous distribution, which is symmetric about its mean $𝜇$. Then the smallest value of $𝑛$ (in integer) such that $𝑃(𝑌1 < 𝜇 < 𝑌) ≥ 0.99$, is ______.

Let $𝑌_1 < 𝑌_2 < ⋯ < 𝑌_n$ be the order statistics of a random sample of size $𝑛$ from a continuous distribution, which is symmetric about its mean $𝜇$. T...

rajveer43

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rajveer43 asked Jan 10

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21

Statistics | Poisson Distribution Sample Question | GATE DA
Let $0, 1, 1, 2, 0$ be five observations of a random variable $𝑋$ which follows a Poisson distribution with the parameter $𝜃 > 0$. Let the minimum variance unbiased estimate of $𝑃(𝑋 ≤ 1)$, based on this data, be $𝛼$. Then $5^4𝛼$ (in integer) is equal to _____________

Let $0, 1, 1, 2, 0$ be five observations of a random variable $𝑋$ which follows a Poisson distribution with the parameter $𝜃 0$. Let the minimum variance unbiased ...

rajveer43

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rajveer43 asked Jan 10

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22

GATE 2021 | Statistics | Q-3

rajveer43

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rajveer43 asked Jan 10

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GATE 2021 | Statistics | Q-11
Let $X$ be a non constant positive random variable such that $E(X)=9$. Then which of the following statements is correct A) $E(1X+1)>0.1$ and $P(X≥10)≤0.9$ B) $E(1X+1)<0.1$ and $P(X≥10)≤0.9$ C) $E(1X+1)>0.1$ and $P(X≥10)>0.9$ D) $E(1X+1)<0.1 and P(X≥10)>0.9$

Let $X$ be a non constant positive random variable such that $E(X)=9$. Then which of the following statements is correctA) $E(1X+1)>0.1$ and $P(X≥10)≤0.9$B) $E(1X+...

rajveer43

96 views

rajveer43 asked Jan 10

3 votes

1 answer

24

GATE IN 2023 | GA Question: 4
Which one among the following statements must be $\text{TRUE}$ about the mean and the median of the scores of all candidates appearing for $\text{GATE }2023?$ The median is at least as large as the mean. The mean is at least as large as ... the candidates have a score that is larger than the median At most half the candidates have a score that is larger than the mean.

Which one among the following statements must be $\text{TRUE}$ about the mean and the median of the scores of all candidates appearing for $\text{GATE }2023?$The median i...

admin

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admin asked May 22, 2023

3 votes

1 answer

25

GATE Civil 2023 Set 1 | GA Question: 7
Which one of the options can be inferred about the mean, median, and mode for the given probability distribution (i.e. probability mass function), $P(x)$, of a variable $x?$ mean $=$ median $\neq$ mode mean $=$ median $=\operatorname{mode}$ $\operatorname{mean} \neq \operatorname{median}=\operatorname{mode}$ mean $\neq$ mode $=$ median

Which one of the options can be inferred about the mean, median, and mode for the given probability distribution (i.e. probability mass function), $P(x)$, of a variable $...

admin

1.3k views

admin asked May 21, 2023

1 votes

0 answers

26

Best Open Video Playlist for Elementary Statistics Topic | Quantitative Aptitude
Please list out the best free available video playlist for Elementary Statistics from Quantitative Aptitude as an answer here (only one playlist per answer). We'll then select the best playlist and add to GO classroom ... are more likely to be selected as best. For the full list of selected videos please see here

Please list out the best free available video playlist for Elementary Statistics from Quantitative Aptitude as an answer here (only one playlist per answer). We'll then s...

makhdoom ghaya

222 views

makhdoom ghaya asked Aug 27, 2022

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