Recent questions tagged probability

ML | DA | Multiclass Classification
Suppose a classifier predicts each possible class with equal probability. If there are 10 classes, what will the cross-entropy error be on a single example? $− log(10)$ $−0.1 log(1)$ $− log(0.1)$ $−10 log(0.1)$

Suppose a classifier predicts each possible class with equal probability. If there are 10 classes, what will the cross-entropy error be on a single example?$− log(10)$$...

rajveer43

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rajveer43 asked Jan 29

1 votes

1 answer

ML | NN | DA Practice
Suppose that you are training a neural network for classification, but you notice that the training loss is much lower than the validation loss. Which of the following can be used to address the issue (select all that apply)? Use a network with fewer layers Decrease dropout probability √ Increase $L2$ regularization weight Increase the size of each hidden layer

Suppose that you are training a neural network for classification, but you notice that the training loss is much lower than the validation loss. Which of the following ca...

rajveer43

160 views

rajveer43 asked Jan 29

1 votes

2 answers

GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 7
Ben participates in a prize draw. He receives one prize that is equally likely to be worth $\$ 5, \$ 10$ or $\$ 20$. Jamie participates in a different prize draw. She receives one prize that is equally likely to be worth $\$ 30$ or $\$ ... $ 50?$ $1 / 6$ $1 / 3$ $1 / 2$ $1 / 4$

Ben participates in a prize draw. He receives one prize that is equally likely to be worth $\$ 5, \$ 10$ or $\$ 20$. Jamie participates in a different prize draw. She rec...

GO Classes

331 views

GO Classes asked Jan 28

6 votes

1 answer

GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 12
Let $x$ be a random variable possessing the probability density function $ f(x)= \begin{cases}c x & , x \in[0,10] \\ 0 & , \text { otherwise }\end{cases} $ where $c \in \mathbb{R}$. The probability that $x \in[1,2]$ is ______. $\dfrac{1}{100}$ $\dfrac{3}{100}$ $\dfrac{5}{100}$ $\dfrac{7}{100}$

Let $x$ be a random variable possessing the probability density function$$f(x)= \begin{cases}c x & , x \in[0,10] \\ 0 & , \text { otherwise }\end{cases}$$where $c \in \ma...

GO Classes

488 views

GO Classes asked Jan 28

4 votes

1 answer

GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 44
Football teams $T_1$ and $T_2$ play two games against each other in the Premier League. It is assumed that the outcomes of the two games are independent of each other. The probabilities of $T_1$ winning, drawing and losing against $T_2$ ... What will be the value of $P(X=Y)?$ $1 / 3$ $13 / 36$ $1 / 36$ $1 / 18$

Football teams $T_1$ and $T_2$ play two games against each other in the Premier League. It is assumed that the outcomes of the two games are independent of each other. Th...

GO Classes

470 views

GO Classes asked Jan 28

1 votes

1 answer

ML | DA | Classification
You encounter a classification task, and after training your network on 20 samples, the training converges, but the training loss is remarkably high. You decide to train the same network on 10,000 examples to address this issue. Is your approach to fixing ... of the model. D) No, a better approach would be to keep the same model architecture and increase the learning rate.

You encounter a classification task, and after training your network on 20 samples, the training converges, but the training loss is remarkably high. You decide to train ...

rajveer43

179 views

rajveer43 asked Jan 27

0 votes

1 answer

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

185 views

rajveer43 asked Jan 27

8 votes

2 answers

GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 6
A college has $10$ (non-overlapping) time slots for its courses, and assigns courses to time slots randomly and independently. A student randomly chooses $3$ of the courses to enroll in. What is the probability that there is a conflict in the student's schedule? (answer upto $2$ decimals)

A college has $10$ (non-overlapping) time slots for its courses, and assigns courses to time slots randomly and independently. A student randomly chooses $3$ of the cours...

GO Classes

829 views

GO Classes asked Jan 21

6 votes

1 answer

GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 36
Let $A, B, C$ be events such that $P(A)=P(B)=P(C)=0.5, P(A \cap B)=0.3, P(A \cap C)=0$. Which of the following is/are true? $P(A \cup B)=0.75$ $P(A \cup C)=1$ $P(B \cap C)=0.23$ $P(B \cup C)=0.9$

Let $A, B, C$ be events such that $P(A)=P(B)=P(C)=0.5, P(A \cap B)=0.3, P(A \cap C)=0$.Which of the following is/are true?$P(A \cup B)=0.75$$P(A \cup C)=1$$P(B \cap C)=0....

GO Classes

869 views

GO Classes asked Jan 21

0 votes

1 answer

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

393 views

rajveer43 asked Jan 16

1 votes

2 answers

AIMT-2 GATE DA 2024| ML Question for GATE | Wanshington Uni | Aug-23 Mid term test
Suppose we are performing leave-one-out (LOO) validation and $10$-fold cross validation on a dataset of size $100, 000$ to pick between $4$ different values of a single hyperparameter. How many times greater is the number of models that need to be trained for LOO validation versus $10$-fold cross validation? Answer:

Suppose we are performing leave-one-out (LOO) validation and $10$-fold cross validation on a dataset of size $100, 000$ to pick between $4$ different values of a single h...

rajveer43

404 views

rajveer43 asked Jan 16

0 votes

1 answer

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

247 views

rajveer43 asked Jan 16

0 votes

1 answer

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

439 views

rajveer43 asked Jan 14

3 votes

1 answer

GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 28
Suppose that $X$ and $Y$ are independent random variables such that each is equal to $0$ with probability $.5$ and $1$ with probability $.5.$ Find $P(X+Y \leq 1)?$ (Answer up to $2$ decimals)

Suppose that $X$ and $Y$ are independent random variables such that each is equal to $0$ with probability $.5$ and $1$ with probability $.5.$Find $P(X+Y \leq 1)?$ (Answe...

GO Classes

526 views

GO Classes asked Jan 13

4 votes

1 answer

GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 29
You have three coins in your pocket, two fair ones but the third biased with the probability of heads $p$ and tails $1-p$. One coin selected at random drops to the floor, landing heads up. How likely is it that it is one of the fair coins? $1 / \mathrm{p}$ $1 /(1+p)$ $p /(1+p)$ $(1+p) / p$

You have three coins in your pocket, two fair ones but the third biased with the probability of heads $p$ and tails $1-p$. One coin selected at random drops to the floor,...

GO Classes

468 views

GO Classes asked Jan 13

0 votes

1 answer

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

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rajveer43 asked Jan 11

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0 answers

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

108 views

rajveer43 asked Jan 11

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GATE 2018 | MATHS | Q-63
Let $X$ be the number of heads in 4 tosses of a fair coin by Person 1 and let $Y$ be the number of heads in 4 tosses of a fair coin by Person 2. Assume that all the tosses are independent. Then the value of $P(X = Y )$ correct up to three decimal places is_________

Let $X$ be the number of heads in 4 tosses of a fair coin by Person 1 and let $Y$ be the number of heads in 4 tosses of a fair coin by Person 2. Assume that all the tosse...

rajveer43

103 views

rajveer43 asked Jan 11

0 votes

1 answer

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

123 views

rajveer43 asked Jan 11

1 votes

1 answer

GATE 2018 | MATHS | Q-48
Let $X_1, X_2, \ldots, X_n$ be independent and identically distributed random variables with probability density function given by \[ f_X(x; \theta) = \begin{cases} \theta e^{-\theta(x-1)}, & \text{if } x \geq 1 \\ 0, & \text{otherwise} \end{cases} \] Also, let $X = \frac{1}{n ... {1}{X}$ (B) $\frac{1}{X^{\frac{1}{\theta} - 1}}$ (C) $\frac{1}{X - 1}$ (D) $X$

Let $X_1, X_2, \ldots, X_n$ be independent and identically distributed random variables with probability density function given by\[ f_X(x; \theta) = \begin{cases} \the...

rajveer43

100 views

rajveer43 asked Jan 11

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