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.

learn more… | top users | synonyms

3
votes
1answer
28 views

Expected value of trials to obtain a red ball in a box of white balls.

I have a problem that involves a box containg N balls, one of which is red and the rest of which (N-1) are white. The question involves finding the expected value and variance for the number of trials ...
0
votes
0answers
37 views

Where can I find this definition of “expected value”?

I need bibliography or some text about this definition: "Define the expected value of a function by: $E_{t}(x(t))=(\frac{1}{t})\int_{0}^{t} x(s)ds$. " I think that it's statistics or functional ...
1
vote
2answers
51 views

Solve $\frac{1}{2^\theta}\sum_{k=0}^{\theta} {\theta\choose k} \delta(k)=\theta$ for $\delta$

The following arises in unbiased estimation of a parameter for the binomial distribution, but that information is not needed for solving the question. I tried solving this by manipulating the sum to ...
0
votes
1answer
24 views

Biased sample from biased sample

A webpage has users, where each user has a number of projects uniquely assigned to him or her. I want a random sample of users by randomly sampling projects and then taking the users connected to this ...
0
votes
1answer
26 views

How can I calculate a campaign goal ongoing?

I work for a non-profit and we are continuing a campaign to serve 1000 children at $29 a month. As of today we have the funds to serve 398 children based on an average from the last 12 months. My ...
0
votes
0answers
6 views

Testing Relative Preference Fit (multi-variable)

I'm playing around with a data set that I have built which is meant to represent the subjective preferences of a person related to a particular product. I want to compare, then, the properties of a ...
0
votes
2answers
39 views

95% Confidence Interval Problem for a random sample

The sample mean of a random sample of $25$ observations is $9.6$ and the sample variance is $22.4$. Derive a $95$ confidence interval for the population mean. I calculated the following: Confidence ...
-1
votes
0answers
8 views

Repeated Measures…(Analysis of Variance) [closed]

What are within-subject variables and what are the difference scores between these variables referred to?
0
votes
0answers
9 views

Estimating Johnson Distribution Parameters by Quantile

In this paper: http://www.researchgate.net/publication/31291960_Quantile_Estimators_of_Johnson_Curve_Parameters the four parameters for the Johnson distribution ...
1
vote
0answers
11 views

the meaning of 4-wise hash function

If someone says: 4-wise independent sign (hash) functions $s_1,s_2, s_3 : [d] → \{+1, −1\}$, then what does it means? I cannot use k-wise Independence variables (the definition 1 ...
-1
votes
0answers
12 views

Hypothesis Testing with given Pearson correlation.

There are two independent sets of samples , female and male. The problem is to calculate the 95 % C.I. of the mean of total( male+ female, two samples) population. -> Female : n=100, mean= 169.1, sd ...
2
votes
1answer
17 views

How to find the degrees of freedom for a chi-square variable

How does one find the degrees of freedom for a Chi-square random variable when trying to fit a distribution to a sample? I read an explanation regarding this in this source. I don't understand how to ...
3
votes
1answer
47 views
+50

Is this alternative hypothesis valid?

Could anyone check that the alternative hypothesis is making sense? I wanted to prove that the "Mahalanobis distance ($\mathbf{(x_i - \bar{x})^T \Sigma^{-1}(x_i - \bar{x})}$)" is a Log Likelihood ...
0
votes
1answer
11 views

Do the bounds change when multiplying a probability distribution by a constant?

Do the bounds change when multiplying a probability distribution by a constant? For example consider when an exponential distribution bounded by upper bound A, lower bound B and mean X, is multiplied ...
1
vote
0answers
51 views

Need simplified formula of probability equation

I have RV $x$ which is function of independent continuous RVs $x_1$ and $x_2$. After some manipulations, I came up with an expression for the outage probability of $x$ as $$P_\text{out}(y)=\Pr(x\leq ...
1
vote
0answers
34 views

Proving Convergence of a Derivative Free Method

Hopefully this question is on topic for the mathematics community (rather than the statistics) since the optimization method I am using relies on a statistical model. Well I am building an algorithm ...
0
votes
1answer
22 views

Univariate Normal Distribution Transformation

X is the time taken for a high school athlete to complete a 100m sprint, in seconds, which follows a normal distribution with a mean of 16. The athlete would complete the sprint under 19.495 seconds ...
1
vote
2answers
21 views

Cost per pound savings analysis between two data sets

Given 2 sets consisting of (type, cost, weight) and grouping the data into sub-sets based on type (for simplicity let's just say their are two types). How would you go about comparing these data sets ...
0
votes
0answers
32 views

black jack variance

Is it correct to compute variance in Blackjack using Bernoulli distribution? For example: $p = 41\%$ is the probability of winning $q = 9\%$ is the probability of tieing $t = 50\%$ is the ...
1
vote
1answer
24 views

Example of a distribution with mode undefined

Is there any distribution with an undefined mode? If all the elements of the data set have frequency 1 is the mode undefined or all the elements are modes of the distribution?
-4
votes
0answers
22 views

probabillity and statisstics [closed]

Thirty percent of all telephones of a certain type are submitted for service while under warranty. Of these, 70% can be repaired, whereas the other 30% must be replaced with new units. If a company ...
3
votes
2answers
51 views
+300

Proof of multivariate regression plane maximizes correlation in normals

I am doing a homework sheet as practice for an upcoming course in multivariate statistics and been stuck on the following problem: Let ...
2
votes
2answers
44 views

Is $P(n) = \frac{a n }{b}$ or $\frac{(a+1) n}{b + 1}$?

I investigated Some random data and I was a bit confused. Could be Mathematical coincidence but i'm not sure. Consider the integers $1,2,3,...,a$ Randomly Pick $b$ dinstinct element out of them. ...
2
votes
0answers
36 views

How to solve this confusing iterative limit equation

I have this equation which is intended to be used on a data set of integers. I am attempting to create a software algorithm using this equation, but I am very confused about how to implement it. ...
0
votes
1answer
81 views

Combinatorics Statistics Probability of a Letter Chain

What formula could help me quantify the probability of a chain of three letters (English Alphabet) where each letter is based on the previous one (stochastic modeling, Markov-chains, probabilities) ...
0
votes
0answers
28 views

How to find the maximum likelihood estimators of an inverse normal distribution?

I'm really struggling to deal with the product of the pdf's for the independent (and identical) samples and come up with the likelihood function. Does anyone know how to get to the likelihood function ...
1
vote
1answer
49 views

Equations for Classification & Probability Problem

There are 4 containers (classes) to keep balls of different colors (red, green, blue, orange). We know that Container A is for red balls because it contains 80% red balls. B for green balls (90%), and ...
-1
votes
1answer
38 views

Senate elections statistics problem [closed]

The upcoming senate elections will be determined by 3 states: Arkansas, Louisiana and North Carolina. Based on NYT predictions, Republicans have the following probabilities of wining each of these ...
6
votes
1answer
33 views

Limit of median of uniform distribution

Let $X_1,X_2,\ldots$ be a random sample from the uniform distribution on the interval $(0,1)$. Assuming that $n$ is odd, find the pdf of the sample median (say $M_n$). Does the pdf of the r.v. ...
-3
votes
2answers
27 views

How to proof that the median of a lognormal distributions equals $\exp(\mu)$ [closed]

If $V$ is lognormal distribution, how can you prove that his median equals $\exp(\mu)$? With $\mu$ the mean of the normal distibuted $\ln(V)$
1
vote
2answers
31 views

Understanding degrees of freedom in relation to rank for $\sum_{i=1}^{n}(y_i-\bar{y})^2$

So I'm looking at this website which states: One of the questions an instrutor [sic] dreads most from a mathematically unsophisticated audience is, "What exactly is degrees of freedom?" It's not ...
-6
votes
0answers
39 views

Random variables and probability [closed]

Number of goals per game is considered as a random variable. In 5 game matches 0 goals have been achieved. In 8 game matches 1 goal has been achieved. In 4 game matches 2 and 5 goals have been ...
0
votes
0answers
19 views

Properties of Fitted Regression Line

Suppose the following regression model $$Y_i=BX_i+\epsilon_i$$ where $\epsilon_i\sim N(0,\sigma^2)$independents is the random error. Verify which properties of the estimated regression line are ...
1
vote
0answers
24 views

Optimal place to measure for simple linear regression/fitting

Suppose I have a linear model $y_i=a\cdot x_i+b+\epsilon_i$, where $y_i,\epsilon_i,a,b\in\mathbb{R}$, $x_i\in[-1,1]$. I can take n measurements of $y_i$ at $x_i$, where $n\in\mathbb{N}$. $\epsilon_i$ ...
1
vote
2answers
39 views

A trivial question about prediction of arrival rate of a Poisson process from sample data

A bus arrives at a bus stop according to a Poisson process. It is given that in the last 100 hours, the bus arrived at the bus stop exactly 200 times. Predict the arrival rate for the bus at the bus ...
1
vote
3answers
82 views

What kind of math is this? Picture

What kind of math is this? Four years of college and I still never came across this. Can you even input this on a calculator? Thank you everyone. You guys rock!
1
vote
1answer
37 views

'Markovian Property' vs 'Memoryless Property'

The two properties have the commonality in the sense that they predict the future based on the current state, not on the whole history of how the process wandered into the state. Then, what is the ...
-1
votes
1answer
77 views

probability of equiprobable events : A, B, C [closed]

If A, B , C are equiprobable events , we determine the possible value Most small to P(A) such a way the probability of occurrence of the three events always simultaneously exceed 0.95. Do I have to ...
0
votes
0answers
12 views

How to continuously computate of tf-idf [closed]

I have a document corpus containing over 4 million documents. Now I want to build an index over terms from the documents of the corpus. Based on the tf-idf of these terms, I want to remove the least ...
0
votes
1answer
15 views

Calculating cumulative error in distribution of elements

I am dealing with a real life situation where I have a distribution of 12 unique elements that can be permutated in any way possible (so 12! = 479,001,600 possible permutations). The index position ...
1
vote
1answer
36 views

How can I calculate area under the curve?

I have problems understanding how can I calculate manually area under the curve for my predictions, knowing the real values. I understand the idea behind confusion matrix, can calculate true ...
0
votes
1answer
18 views

Comparing two random sets of numbers vs. one random, one fixed

I'm trying to run some basic simulations of if one thing can randomly guess another (is the intersection of two sets non-null) and I'm curious if different implementations in software (which are very ...
0
votes
1answer
17 views

Probability of two sets of plates

So about a day or two ago i was driving and saw another car with a license plate almost identical to mine, so i asked myself the following questions: 1)What is the probability that 2 license plates ...
0
votes
0answers
32 views

Probabilities in this blackjack variation

Let's say I play blackjack (52 cards, figures count for 10, aces count for 1 or 11) and alone (no dealer). The cards I use for one particular game are always removed at the end of that game and won't ...
1
vote
1answer
20 views

Is p value sufficient to compare the significance

What we have is the following: Three groups of students are taking the same pre-test and post-test on a Math subject. In between they get to play with tutoring system A (for first group), tutoring ...
1
vote
0answers
47 views

What is the probability that TEAM A will win in both of the following scenarios?

Two teams are in the same league and just finished a season. Assume both teams had played the exact same schedule. TEAM A had a winrate of 90% and TEAM B had a winrate of 70%. If both teams then meet ...
0
votes
1answer
23 views

Can we use a single sample from a population to create confidence intervals, do hypothesis testing, etc.?

When conducting confidence intervals, hypothesis testing, and ANOVAs are we using the sampling distribution with multiple samples as opposed to a single sample? Are there cases where we use just a ...
3
votes
2answers
57 views

Distribution of sum of 2 circular uniform random variables

I hope you can help me resolve the following problem: Let $\Phi_1$ and $\Phi_2$ circular uniform random variables such that $0\leq\Phi_i\leq 2\pi$ (with $i=1,2$). Then the probability density ...
2
votes
1answer
23 views

Explanation for “jointly pdf is constant but marginal pdf is not”

Consider: $X,Y \sim \text{uniformly distributed in }(0 \leq y \leq x \leq 1)$ From short computation, we know: Jointly pdf: $f_{XY}(x,y) = 2$ Marginal pdf of $x$: $f_{X}(x) =\int_0^x ...
0
votes
0answers
11 views

What is the difference between ANOVA and ANOVA decomposition?

I was reading the paper about ANOVA decomposition http://faculty.bscb.cornell.edu/~hooker/fame_jcgs.pdf but I can't see how it is related to ANOVA. (Except that we have mutual orthogonality between ...