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.

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Calculating uncertainties before aproximating exponential function

I have a table of values that are supposed to be used as points for exponential regression (least squares method). Values in both columns are uncertain, which means that the function itself is a ...
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12 views

Calculate total revenue share

Suppose you have data such as this: January Total minutes of all videos watched: 50 Total minutes of video X watched: 25 Total revenue: 200 February Total minutes of all videos watched: 200 Total ...
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14 views

A distribution that is skewed to the left

Suppose that you and your friends emptied your pockets of coins and recorded the year marked on each coin. The distribution of fates would be skewed to the left. Explain why.
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12 views

What percentage of all stocks lost money?

A return less than zero means that owners of the stock lost money. About what percentage of all stocks lost money?
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11 views

Sketch line graphs

Sketch line graphs of a series of observations over time having each of the following characteristics. Mark your time axis in years. (a) A strong downward trend, but no seasonal variation (b) ...
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15 views

Given a joint PDF verify that it is a joint density function

The function from f(x,y) is represented below where 0 < x < 1 and 0 < y < 2 ...
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8 views

Multiple dependant statistical probabilities

How do I calculate probabilities based on each other, for example. If var1 has a probability of 47% , var2 has a probability of 36% if var1 is true, and 0% if false, and var3 has a probability of 23% ...
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7 views

asymptotic unbiasedness of weibull mle

It's known that the MLEs of the two-parameter Weibull distribution scale and shape parameters are not available in a closed form. It is, however, known that they do exist, are unique, and moreover, ...
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2answers
15 views

Confidence Interval has no relation to the probability?

An Intro to Stats class has the following problem: Find and interpret the 90% confidence interval for the true mean The provided answer is this: ...
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3 views

Kruskal Wallis Test Ranking

I have a simple question. I have data which contains one zero and I'm about to rank all the data using excel. Do I need to ignore this one zero value? So that I need to subtract 1 from the entire ...
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1answer
25 views

$X$ normally distributed in $\mathbb R^n$ iff components $x_i$ normally distributed?

We've had the normal distribution today in class and I was thinking about the following: Let $X$ be normally distributed, $X\sim N(a,\Sigma)$ with a symmetric positive definite matrix $\Sigma$ and ...
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1answer
10 views

Finding Multiple regression coefficients

If I have a multiple regression like this $Y=a+b_1.X_1+b_2.X_2,$ how can I calculate the values of $b_1$ and $b_2$? I have searched on the web but couldn't find an answer.
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Uniform distribution over a set R in the x-y plane and let P be the family of distributions obtained by letting R range over a class T of sets R

So the question is, Let T be the set of all triangles with sides parallel to the x-axis, the y-axis and the line y = x respectively. Find a minimal sufficient statistic and prove that it is minimal ...
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14 views

How to correctly calculate and represent change/delta?

I am a software engineer, and I am generating a report of changes in numbers. I would like to know the correct/standard way of calculating, representing, and displaying the change/delta. For example, ...
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13 views

Multiple regression equation

Can someone please recommend me a good book to understand multiple regression? I need to know how to calculate the equation of multiple regression with two independent variables The one I have does ...
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13 views

The mean of a deterministic sequence

could someone explain to me why the expected value of $y(n)$ is the following: $\operatorname{E}(y(n)) = f(n)$ when $y(n) = x(n) + f(n)$ and $x(n)$ has zero mean. But why is the expected value of a ...
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2answers
7 views

Calculate confidence interval

The distribution of days that are required to complete a certain activity can be approximated by a standard normal distribution with a mean of 500 days and a standard deviation of 12 days. What ...
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16 views

Three proportions testing null hypothesis

I have the following question. In a random sample of 250 people with low incomes, 155 are in favour of a new piece of legislation, while in random samples of 200 people with average incomes and 150 ...
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1answer
19 views

Finding the MLE for a given function [on hold]

What is the MLE for $f(x) = (\theta+1) x^\theta$ where $0 \leq x \leq 1$
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16 views

Uniform Distribution Min & Max unbiased estimators?

I have $n$ samples ($iid$) from a uniform distribution over $[a,b]$ with unknown $a$ & $b$, let call them $x_i$. Let $Min\{x_i\}=\hat{a}$ and $Max\{x_i\}=\hat{b}$. What are unbiased estimators ...
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14 views

Using Convolution to find density of sum of non-independent normal densities

$X_1 \sim N(\mu_1, \sigma_1^2)$ and $X_2 \sim N(\mu_2, \sigma_2^2)$. The $X_i's$ are not independent. Let $Y = X_1$ + $X_2$. Then, $ \begin{align*} f_Y(y) &= \int_{0}^{y} ...
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3answers
34 views

Suppose you roll a pair of fair dice. What is the probability that the number of dots on the two dice sum to either $5$ or $10$?

Suppose you roll a pair of fair dice. What is the probability that the number of dots on the two dice sum to either $5$ or $10$? (a) $5/36$ (b) $7/36$ (c) $11/36$ (d) $4/36$ So here are the possible ...
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1answer
23 views

Correct Way to Break Up Range Into N Approximately Equal Discrete Bins

This seems simple, but none of the solutions I've tried work well. For example, for a range [0, 67), how can you split it up into 20 approximately equal sized discrete bins without introducing ...
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13 views

Auto-correlation calculation

Is auto correlation of lag $k$ the same as auto correlation of order $k$? If not, how do their formulas differ? For lag $k$ is the denominator: $\sum_1^n(x_t-\bar{x})^2$. For order $k$ is the ...
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5 views

Statistics, Chapter random variables and discrete probability distributions [on hold]

An elementary school teacher learned that 35 percent of school age children have at least 3 cavities. The teacher has 30 students in his class. What is the standard deviation? (Round your answer(s) to ...
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17 views

Var(Y_{i}) = σ^{2})

In the system regresion the supose that: 1) $E(\epsilon_{i}) = 0$ 2) $Var(\epsilon_{i}) = \sigma^{2}$ $E(Y_{i})=\beta_{0}+\beta_{1}\times X_{i1} + \ldots + \beta_{p}\times X_{ip}$ How I prove that ...
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32 views

Probability Assignment to Intervals in $\mathbb{R}^{n}$.

Given a random variable $\bf{X}$ distributed on $\mathbb{R}^{n}$, let $F_{X}(t)$ be its distribution function. Suppose we want to find $P\left(\textbf{X} \in (\textbf{a}, \textbf{b}]\right)$. I was ...
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1answer
26 views

Cumulative distribution function of exponentials

I have the cumulative distribution function $F(x)=(1-e^{-x})\mathbb{1}_{x≥0}$ and want to write the CDF to $F(\frac{x-\mu}{\sigma})$. I have derived ...
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26 views

What is the variance E[A]^2, statistics? [on hold]

$x(t)= A_i$, for $i \leq t < i + 1$ and $\{i = 0, 1 ,2 ,3,.....\}$. $A_i$ are independent variables, pmf of $P(A_i = 1) = P(A_i = -1) = 1/2$. Find the variance $E[A]^2$. I am so stuck on this ...
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2answers
17 views

Probability Distribution Function?

An urn contains 8 green balls and 17 yellow balls. A ball is drawn from the urn and its color is noted and then the ball is placed back in the urn. 5 balls are drawn this way. Let $X$ denote the ...
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1answer
27 views

How to compute the question [on hold]

The senior sales agent for Regional Real Estate Company closes a deal 71.5% of the time. a) If the manager believes that the agent will see 14 prospective buyers next week, what is the probability ...
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1answer
21 views

Likelyhood of Poisson Distribution

The number of accidents in a week follows a poisson distribution with mean $\lambda$. Likelyhood is given as $$L(\lambda)=\frac{ \lambda^{\sum_1^n x_i } e^{-n\lambda}} { \prod x_i!}$$ However only ...
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12 views

Predictive analysis based on history

Let me first say that I am a CS person and my knowledge about statistics is quite basic. I am trying to see what predictive analysis to use for a problem I am trying to solve. I will try to make my ...
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24 views

Predicting profit with price variation

I am currently working on a high school project that aims to predict profit from X amount of items to Y amount of profit based off a deviated sale price. For instance: I sale 10 cookies for 10 ...
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22 views

Normal probability distrubution.

any student who scores in the top 4% of students on the SMRT standardized exam. SMRT scores have a mean of 260 and a standard deviation of 22. What score does a student need to attain in order to ...
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14 views

Second derivatives of MLE to multivariate normal distribution

I want to calculate the second derivatives to the MLE's $\hat{\mu}$ and $\hat{\Sigma}$ to confirm that the extremums indeed are maximums to the multivariate normal distribution $$ ...
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1answer
26 views

Probability that an event will occur X times in a row at any point in Y trials?

Event AA has a $60\text{%}$ failure rate. Given $256$ trials, what is the probability that at some point event AA will fail $9$ times in a row? Is there a formula that is fairly plug-and-play? I ...
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1answer
20 views

How to find the PDF from the CDF?

I have the following CDF: F(x)= \begin{cases} 0 & \text{if } x < 4 \\ \frac{x-4}{4} & \text{if } 4 \le x < 8 \\ 1 & \text{if } x \ge 8 \end{cases} I know that the PDF is equal to ...
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3answers
70 views

Show that $P(X=c)=1 $for some constant c

Suppose $X$ and $Y$ are independent random variables, also $X$ and $X-Y$ are independent. Prove that $$P(X=c)=1$$ for some constant c. I tried using moment generating function, please give me some ...
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1answer
23 views

A joint pdf question [on hold]

I need help over a question. I appreciate all helps.Thank you.
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1answer
13 views

Sampling distributions question

LEt x bar be the mean of a random sample of size n=48 from the uniform distribution on the interval (0,2); that is, f(x) =1/2 for 0 for this problem i am confused because don't we need to know mean ...
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23 views

In 60,000 CABG surgeries, what is the expected number of retained foreign bodies? I cant figure out where I am going wrong on this.

In CABG surgery, there is a 0.00015 probability of a retained foreign body (e.g., a sponge or a surgical instrument) left inside the patient. (a) In 60,000 CABG surgeries, what is the expected ...
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16 views

In Northern Yellowstone Lake, earthquakes occur at a mean rate of 1.3 quakes per year. Let X be the number of quakes in a given year. [on hold]

In Northern Yellowstone Lake, earthquakes occur at a mean rate of 1.3 quakes per year. Let X be the number of quakes in a given year. (a) Justify the use of the Poisson model. ...
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20 views

recognize the distribution corresponding to this characteristic function

The characteristic function of a random variable X is given as $$\frac{3+cos(t)+cos(2t)}{5} $$, what is the distribution of X? I was thinking of the discrete random variable X=,0,1,2 with mass ...
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1answer
22 views

What is the probability that all are eligible? What is the probability that at least one is ineligible? [on hold]

Past insurance company audits have found that 2 percent of dependents claimed on an employee’s health insurance actually are ineligible for health benefits. An auditor examines a random sample of 10 ...
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Uni-variate Moving Average Theta coefficients

Consider the Uni-variate Moving Average Models (MA models) MA(1) $$x_t = \mu + w_t +\theta_1w_{t-1}$$ or the second order moving average MA(2) $$x_t = \mu + w_t +\theta_1w_{t-1}+\theta_2w_{t-2}$$ ...
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Multiplying/dividing mean and std dev of two different values

I'm working on predicting outcomes of games given statistics from the two teams involved. Two of the statistics I have are below: AGA (average goals against): The arithmetic mean of number of goals a ...
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15 views

Contingency table with a 0 value in a concrete problem.

I don't know how to deal with this problem: In order to evaluate the relationship with a risk factor and a disease we have the following case-control study: \begin{array}{|c|c|c|} \hline Risk Factor ...
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2answers
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What is the expected value of the mean of the highest $m$ numbers in a population of $N$ normally distributed random variables?

Suppose that I randomly generate $N$ numbers according to the standard normal distribution, $\mathcal{N}(0,1)$. Then suppose I pick the highest $m$ numbers, $x_1\leq x_2 \leq \cdots \leq x_m$. ...
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1answer
21 views

Could not find right formula for Conditional Probability [on hold]

P(A) = 0.20 P(B) = 0.62 Assuming that A and B and mutually exclusive, the conditional probability $P(A|B^c)$ is equal to... A) 0.769 B) 0.797 C) 0.948 D) 0.526 I've tried all the formula but I ...