# Tag Info

Accepted

### Two dice rolls - same number in sequence

The probability of rolling a specific number twice in a row is indeed 1/36, because you have a 1/6 chance of getting that number on each of two rolls (1/6 x 1/6). The probability of rolling any ...
Accepted

### What is the derivative of the ReLU activation function?

The derivative is: $$f(x)= \begin{cases} 0 & \text{if } x < 0 \\ 1 & \text{if } x > 0 \\ \end{cases}$$ And undefined in $x=0$. The reason for it being undefined at $x=0$ is ...
• 2,192

### Two dice rolls - same number in sequence

To make it perfectly clear, consider the sample space for rolling a die twice. (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (...
• 721

### How can I prove mathematically that the mean of a distribution is the measure that minimizes the variance?

Budding statisticians in Statistics 101 with no mathematical skills beyond high-school algebra should consider \begin{align} E\left[(X-a)^2\right] &= E\bigr[\big(X-\mu + \mu -a\big)^2\bigr] & {...
• 47.2k

### Find expected value using CDF

The result extends to the $k$th moment of $X$ as well. Here is a graphical representation:
• 2,601

### What are the branches of statistics?

I find these classification systems extremely unhelpful and contradictory. For example: neural networks is a form of supervised learning Calculus is used in differential geometry Probability theory ...
Accepted

### Derivation of change of variables of a probability density function?

Suppose $X$ is a continuous random variable with pdf $f$. Let $Y=g(X)$, where $g$ is a monotonic function. The function $g$ could be either monotonically increasing or monotonically decreasing. If $g$ ...
• 2,107

### Interview question: If correlation doesn't imply causation, how do you detect causation?

There are a few ways around this. You are right that A/B testing is one of these. The economics Nobel this year was awarded for the pioneering of field experiments in the study of policies against ...
• 938

### Visually interesting statistics concepts that are easy to explain

I like images illustrating how different patterns can have similar correlation. The ones below are from Wikipedia articles on correlation and dependence and Anscombe's quartet with correlations of ...
Accepted

### A meeting has 12 employees. Given that 8 of the employees are female, what is the probability that all employees are female?

The confusion comes from the fact that there are multiple ways to interpret "Given that 8 employees are female": If it's 8 specific employees - say, the employees in positions 1 thru 8 - ...

### Visually interesting statistics concepts that are easy to explain

Simpson's Paradox A phenomenon that appears when a key variable is omitted from the analysis of a relationship between one or more independent variables and a dependent variable. For instance, this ...

### What are the branches of statistics?

This is a minor counterpoint to Rob Hyndman's answer. It started off as a comment and then grew too complex for one. If this is too far from addressing the main question, I apologise and will delete ...

### probability of one random variable being greater than another

This question is now old enough that I can give you a solution without ruining your homework. As you have pointed out in your question, to compute this probability, you need to find the distribution ...
• 129k

### Is a neural network essential for deep learning?

This is a good question. Is a neural network essential for deep learning? Yes, your teacher provided you with a correct definition of deep learning. You can still do machine learning (a broader ...
• 8,836

### What's the difference between logistic regression and perceptron?

In short, logistic regression has probabilistic connotations that go beyond the classifier use in ML. I have some notes on logistic regression here. The hypothesis in logistic regression provides a ...
• 26.6k

• 611

### Visually interesting statistics concepts that are easy to explain

How does a 2D dataset where the mean of X is 54 with a SD 17, and for Y 48 and 27, respectively, and the correlation between the two is -0.06? Introducing the Anscombosaurus: And its companion, the ...

### Probability of flipping heads after three attempts

There is a slightly easier approach. Since you asked not to be given the answer, here are some hints: In effect you flip each coin up to three times. If it comes up heads on any of those then you ...
• 40.6k

### Is a neural network essential for deep learning?

I'm going to disagree with the other answers. Fundamentally, I would say that deep learning is defined by a hierarchy of learned representations, and not by which particular model is used to define ...
• 4,600
Accepted

### SelectKBest - Feature Selection - Python - SciKit Learn

No, SelectKBest works differently. It takes as a parameter a score function, which must be applicable to a pair ($X$, $y$). The score function must return an array ...
• 566
Accepted

### Causal effect by back-door and front-door adjustments

The action $do(x)$ corresponds to an intervention on variable $X$ that sets it to $x$. When we intervene on $X$, this means the parents of $X$ do not affect its value anymore, which corresponds to ...
• 12.6k