# Tagged Questions

Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and analysis.

76k views

### How to calculate percentile? Is it possible to get 100 percentile?

How do we calculate percentile? I think it should be calculated as: P = Total number of candidates L = Number of candidates whose marks are below yours ...
10k views

### How to use stars and bars (combinatorics)

How to use the stars and bars method? Say I want to find number of combinations I can get with $x_1+x_2+x_3+x_4=22$, where $x_i\in\mathbb{N}$. Is this the correct time to apply the method?
3k views

### How can I calculate “most popular” more accurately?

I'm developing a website at the moment. The website allows users to "rate" a post from 0 to 5. Posts can then be displayed in order of popularity. At the moment, my method of calculation is pretty ...
3k views

### Generalization of variance to random vectors

Let $X$ be a random variable. Then its variance (dispersion) is defined as $D(X)=E((X-E(X))^2)$. As I understand it, this is supposed to be a measure of how far off from the average we should expect ...
115 views

### If $X \sim N(0,1)$, why is $E(X^2)=1$?

If $X$ is a normally distributed with mean $0$ and variance $1$, expectation of $X$ equals $0$ but why is $E(X^2)=1$?
5k views

### What does it mean when a statistician says I’m 90% confident that the mean of the population is between 1 and 9?

Does that mean if I draw samples from the population that 90% of the time I'll get a number between 1 and 9? Added: assume normal distribution for the population.
945 views

### What is the expected number of runs of same color in a standard deck of cards?

Standard deck has $52$ cards, $26$ Red and $26$ Black. A run is a maximum contiguous block of cards, which has the same color. Eg. $(R,B,R,B,...,R,B)$ has $52$ runs. $(R,R,R,...,R,B,B,B,...,B)$ has ...
809 views

### How to quantify the differencen between 2/4 and 20/40?

Assume I have two methods to do prediction. The first method makes 4 predictions and 2 out of 4 are correct. The second method makes 40 predictions and 20 out of 40 are correct. The prediction ...
632 views

### How do you estimate the mean of a Poisson distribution from data?

I have thought of three different approaches for estimating the mean for a Poisson, but I am not sure which one is the correct method to estimate it (the third one is documented separately at the end ...
5k views

### What does -1.13 times faster mean?

I'm reading High Performance JavaScript, and I think the graphs in one chapter are just plain wrong. Here is one on Google Books. The y axis is "Times faster", and it runs from -1.5 to +4.0. Now, I ...
609 views

### How do I calculate the odds of a given set of dice results occurring before another given set?

Dice odds seem simple at first glance, but I've never taken a Calculus based statistics course or game theory, and I think I may need to in order to solve some of the things I'm trying to solve. I can ...
6k views

183 views

### What is a good measure of “controversy”, given a support score and opposition score?

Suppose I have a topic or discussion, and a number of "support" and "opposition" points on each side (You can also think of them as "upvotes" and "downvotes") and I want to calculate a score of how "...
11k views

### Defective items probability question.

Hi I'm working with probability as part of an engineering course, and I'm struggling with the following tutorial question: Components of a certain type are shipped to a supplier in batches of ten. ...
4k views

### Example of Sufficient and Insufficient Statistic?

I am having trouble understanding the concept of a sufficient statistic. I have read What is a sufficient statistic? and Sufficient Statistic (Wikipedia) Can someone please give an example of: a ...
1k views

### What is the expected number of dice one needs to roll to get 1,2,3,4,5,6 in order?

If I have a fair die and throw it until I get a run of 1,2,3,4,5,6 in order, how many times on average must I throw the dice?
6k views

### Kendall tau calculation

Can someone explain how the Kendall tau works? I can't seem to find a good explaination/tutorial/example. I've been running corr(x,y,'kendall') from Matlab's ...
3k views

### pairwise correlation of three random variables

Assume three random variables have all equal pairwise correlation. What are the possible values of this correlation? Can all of these values be achieved? The solution says $\rho \in [-\frac 12,1]$, ...
509 views

### Is there a way to check the correctness of your answer to a probability question?

In CS, there's a systematic way to check if your code is buggy or not as you write code. Is there a way to check the correctness of your answer to a probability question without using a textbook? For ...
448 views

### Function of a random variable: expectation

Let $\{X_i\}_{i=1}^n$ be a sequence of i.i.d. random variables (i.e. a random sample) with pdf: $$f_X(x) = e^{-(x-\theta)} \, e^{-e^{-(x-\theta)}} · \mathbf{1}_{x\in \mathbf{R}}$$ The goal is ...
760 views

I've been reviewing my probability and statistics book and just got up to continuous distributions. The book defines the expected value of a continuous random variable as: $E[H(X)] = \int_{-\infty}^{\... 2answers 422 views ### expectation of$ \left(\sum_{i=1}^n {x_i} \right)^2 $If$x_i$is exponentially distributed$(i=1,...,n)$with parameter$\lambda$and$x_i$'s are mutually independent, what is the expectation of$\left(\sum_{i=1}^n {x_i} \right)^2$in terms of$n$and ... 2answers 121 views ### Which theory is used to calculate the position and energy of a point source? Consider an empty room with one point source that emits a stationary signal (constant sound, radioactive radiation, ...). The energy nor the position of the point source is known. We send someone in ... 5answers 140 views ### Intuitive explanation for dividing by n-1 when calculating sample variance? [duplicate] I understand how to mathematically show that the sample variance (that involves dividing by n-1) is an unbiased estimator of the population variance (which divides by n), and the mathematics has been ... 3answers 145 views ### Chances of someone being of a certain gender at websites I have 2 of websites and I know the chances of a visitor being a female or male. Let's say I have 2 website where the chance of a new visitor being a female is 80%. If the visitor comes on website 1 ... 2answers 670 views ### How to find a confidence interval for a Maximum Likelihood Estimate My cousin is at elementary school and every week is given a book by his teacher. He then reads it and returns it in time to get another one the next week. After a while we started noticing that he was ... 1answer 12k views ### The expectation of absolute value of random variables I need some help with the following problem: Let$X_1,...,X_n$be a random sample from Normal$(0,1)$population. Define $$Y_1=| {{1 \over n}\sum_{i=1}^{n}X_i}|, \ Y_2={1 \over n}\sum_{i=1}^{n}|... 2answers 1k views ### The Birthday Problem I've been reading about the birthday problem which, as I'm sure many of you will know, is a statistical problem which aims at finding out the how many people you would need in a random group to be ... 1answer 356 views ### Is there an introduction to probability and statistics that balances frequentist and bayesian views? Perhaps, roughly, I might be described as advanced undergraduate regarding mathematics. However, I have not learned statistics and have only learned elementary probability. Does there exist a book or ... 2answers 286 views ### What is a confidence interval? What are the nature and purpose of confidence intervals? 2answers 3k views ### Probability/Combinatorics Problem. A closet containing n pairs of shoes. A closet contains n pairs of shoes. If 2r shoes are chosen at random, (where 2r < n), what is the probability that the chosen shoes will contain no matching pair? I have tried thinking about this ... 1answer 1k views ### Probability of Monkey typing keyboard A monkey types at a 26-letter keyboard with one key corresponding to each of the lower-case English letters. Each keystroke is chosen independently and uniformly at random from the 26 possibilities. ... 1answer 3k views ### Given every horse's chance of winning a race, what is the probability that a specific horse will finish in nth place? I have been interested in calculating a specific horse's chance of finishing in nth place given every horse's chance of winning in a particular race. i.e. Given the following: ... 2answers 3k views ### The probability of a drunk person/random walk A drunk person wonders aimlessly along a path by going forward 1 step and backward 1 step with equal probabilities of \frac12. a) After 10 steps, what is the probability that he has moved 2 steps ... 1answer 2k views ### Distribution of Sum of Discrete Uniform Random Variables I just had a quick question that I hope someone can answer. Does anyone know what the distribution of the sum of discrete uniform random variables is? Is it a normal distribution? Thanks! 2answers 617 views ### Bag with infinite number of colored balls Consider a situation with a bag with infinity number of balls. Each ball is of some color. Number of colors is finite but it is not known. Balls are drawn from the bag one by one and checked for the ... 1answer 89 views ### Order statistics for discrete uniform random variables Let X_i, i=1,\cdots,N be i.i.d. discrete uniform random variables, taking values in the range \{0,1,...,M-1\}. Let X_{(i)} denote the i-th order statistic. What are the values of \... 1answer 106 views ### L^1 convergence of PDFs vs L^2 convergence of CDFs Let f_n denote a sequence of PDFs, and F_n denote the corresponding sequence of CDFs. Given L^1 convergence of the PDFs to some PDF f,$$\int_\mathbb{R} |f_n(x) -f(x)| dx \rightarrow 0$$... 3answers 168 views ### Are there order statistics for a Gaussian variable raised to a power? Let$X$be a random variable with a standard normal distribution. Let$Y = |X|^{2p}$. I am trying to find the distribution for$Y_{(n)}$, i.e., the largest value of$Y$out of$n$samples. I have ... 1answer 199 views ### Concentration inequality for sum of squares of i.i.d. sub-exponential random variables? Suppose$X_1, X_2, \ldots, X_n$are independent and each has the same distribution with a sub-exponential random variable$X$(for example,$X$is the square of a standard normal Gaussian variable). ... 3answers 80 views ### distribution of one random over the sum of random variables Suppose that$X_1,\ldots,X_n$are independent random variables with$X_i\sim Gamma(\alpha_i,\beta)$. Define$U_i=\frac{X_i}{X_1+\cdots+X_n}$for$i=1,2,\ldots,n$. Show that$U_i\sim Beta(\alpha_i,\...
I'm trying to understand the concept of degrees of freedom in the specific case of the three quantities involved in a linear regression solution, i.e. $SST=SSR+SSE,$ i.e. Total sum of squares = ...