Recent questions tagged statistics

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...

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

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 like...

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 ...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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 estima...

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+1)<0...

Given below are two statements:Statement I: The risk of rejecting the null hypothesis when it should be confirmed, is more at $0.05 \mathrm{p}$-level than at $0.01 \mathr...

Given below are two statements:Statement I: A Cohort is a population whose members have some specific characteristics in common.Statement II: In a prospective study, the ...