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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stochastic model [closed]

I am trying to simulate a model using ssa for a selection of initial values and be able to discuss the results. can anyone let me know if my code make sense? Basically, it's a simple SIR model over ...
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2answers
38 views

Statistic question (probability)

A suburban town is made up of 36 % low-income 43 % medium-income, and 21 % high-income households. It is known that 82 % of the low-income, 55 % of the medium- income, and 2 % of the ...
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16 views

Conditional variance and mean

The random variables $X$ and $Y$ have the following distribution. $$\begin{array}{lr|rrr|l} &&&Y\\ &f(x,y)&0&1&2&f(x)\\ \hline &0&1/6&2/9&1/36&\\ ...
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1answer
31 views

Probability Question in Statistic

Individuals in a certain population have a $39\%$ probability of contracting disease $A$ and a $21 \%$ probability of contracting disease $B$, and a probability of $4\%$ of contracting both diseases ...
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to be 99% certain of making a profit? central limit theorem?

Let $X_i$ be the profit card $i$ makes when its sold. I let $S_n = X_1 + ... + X_n$ so total profit. I found the mean of $X$ to be $0.1$. and $E[X^2] = 25$ so variance $= 24.99$ Are these correct? ...
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23 views

Calculating the Z-multiplier and Standard Error in Confidence Intervals

If someone can explain the process of working out the z-multiplier of the z-table. I mean, how do we actually calculate instead of looking up on the table? (my primary question) Also how do you ...
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11 views

Assigning a numerical value to clarity [closed]

Is there any way you could assign a numerical value to clarity of sound? For example, if you wanted to see how clarity of sound was affected by environmental factors (being outside, for example), over ...
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1answer
46 views

books on the application of linear algebra on statistics/finance/machine learning

I am reading "linear algebra done right" by Axler and like it a lot. One thing though, in the end I would like to put these theory to use and as a math textbook it doesn't cover much application. ...
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1answer
13 views

Convergence in distribution example

I have a trouble understanding how below is true: I have drawn $F_{\frac{Y_n}{n}} (y)$ above. Is this correct? Now, if I send n to infinity, I still get the same graph (discrete) and not the ...
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19 views

Why are Indicator Random Variables better that Random Variables when analyzing algorithms?

I understand the idea behind a random variable and the indicator random variable. BUT my question is why use indicator random variables if we have random variables? How do these indicator random ...
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2answers
21 views

Reason for defining a quantity with “inf”

In some applications (in my case statistics) I find quantities defined using "inf", e.g. $ ABC = \inf\{x|F_X(x)\ge\alpha\}$ Why not define simply: $F_X(x=ABC) = \alpha$ I imagine it has something ...
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1answer
58 views

The smallest girl in the world

When my daughter was born, she was pretty small: 5lb 14oz. We were told that put her at exactly second centile for non-prem girls. At one point, I asked the doctor whether we should be worried, and ...
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1answer
32 views

if the probability density of $x$ is given by

If the pdf of $X$ is given by $$f(x)=\begin{cases} 1+x & \text{for } -1< x \leq 0 \\ 1-x & \text{for } 0<x<1 \\ 0 & \text{else} \end{cases}$$ and $U=X$ and $V=X^2$ then show ...
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10 views

Standard deviation on population vs sample

I have a problem in which I'm not sure whether to use the formula for standard deviation for a population, or standard deviation for a sample. The problem goes as follows: "Taxes: The increases of ...
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1answer
26 views

asymptotic normality and unbiasedness of mle

Suppose $\hat{\theta}_n$ is the MLE for some parameter $\theta$. Suppose also that the MLE is such that the Cramer regularity conditions are fulfilled, and $\hat{\theta}_n$ is asymptotically normal ...
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15 views

Calculating a covariance word problem

Let X denote the size of a surgical claim and let Y denote the size of the associated hospital claim. An actuary is using a model in which $E(X)=5$, $E(X^2)=27.4$ $E(Y)=7$ $E(Y^2)=51.4$ ...
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47 views

Normal distribution in nature

I applied for a job as a mathematician. In one of the test questions they asked the following: Why normal distribution is so common in nature? What do you think?
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20 views

Convergence in distribution of exponential [closed]

Let ${X_1, X_2,..X_n }$ be random variables which are independent and having the same exponential distribution with density function: $$f(x) = \begin{cases} \alpha e^{-\alpha{x}} & ...
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17 views

Is any triangular matrix with positive diagonal elements a Cholesky factor?

I'm having a hard time finding information about Cholesky factors, and I'm sure it's a very simple question if it was asked to the right person. I need to create positive semi-definite matrix using ...
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21 views

Finding a copula of beta distributions

Consider two given beta-distributed random variables $X_1, X_2$ with cumulative distribution functions $F_1, F_2$ and a given value of "dependence" $\rho \in [-1,1]$. I want to find a copula $C$ for ...
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X,Y uniform distribution (0,1) what is the pdf of X+Y [closed]

X,Y are independent uniform distribution (0,1) what is the probability density function of X+Y
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1answer
17 views

Joint PDF transformation

I think I know how to do this but I just want to make sure that it's 100% correct. $X_1, X_2$ are i.i.d. random variables with distribution EXP(1) f($x_1, x_2$) = $e^{(-x_1-x_2)}$I(x >= 0) ...
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Joint PDF of Chi-Square & Normal Distribution

Let the independent random variables X1 and X2 be N(0,1) and $\chi^2(r)$, respectively. Let $Y_1$ = $X_1/sqrt(X_2/r)$ and $Y_2$ = $X_2$ a) Find the joint pdf of $Y_1$ and $Y_2$. b) Determine the ...
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2answers
26 views

Getting the cumulative distribution function for Sqrt(X) from the cumulative distribution function for X

I've a data set X which consists of randomly generated numbers. My aim is to plot the cumulative distribution function for square root of X without generating data set for square root of X. I'm using ...
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1answer
18 views

Finding variance and standard deviation of a random variable in an equation

Suppose that X is a random variable with mean 17 and standard deviation 5. Also suppose that Y is a random variable with mean 45 and standard deviation 11. Find the variance and standard deviation of ...
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Confidence Lower Bound for a random sample.

IQ scores are desinged to be normally distributed with standard deviation 15. Below are the IQ scores of a random sample of 30 seventh grade girls in a Midwest school district. 114, 100, 104, 89, ...
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1answer
41 views

exactly k consecutive heads, n tosses

What is the expected number of strings of exactly k consecutive heads if a fair coin is tossed n times? My current answer is $$ {n-1\choose k} (\frac{1}{2})^{(k-1)} $$ Is this correct? A possible ...
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20 views

Coin Tossing Probability

A.) I flip a coin ten time and it comes up heads each time. You can clude that there is something weird about that coin. Is this an example of descriptive or inferential statistics? - Inferential ...
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1answer
23 views

Finding the mean of a random variable in an equation given standard deviation and mean

Please help! What do I plug into these equations to solve for the mean of Z?? Suppose that X is a random variable with mean 23 and standard deviation 5. Also suppose that Y is a random variable with ...
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2answers
24 views

Expected number of sides of a dice

I have two dice, one with m sides (labeled 1,2,...m) and one with n sides (labeled 1,2,...n). I roll both three times. The m-sided one comes up 1, 2, 9 and the n-sided one comes up 7, 7, 8. Which is ...
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1answer
38 views

Probability of red M&Ms

Assume that red M&Ms are 10% of all M&Ms. There are 18 M&Ms in a pack. Each pack is a random sample of the population of M&Ms. What is the probability of a pack with no red ...
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1answer
15 views

Calculation of median

I want to calculate the median of several variables. The detail is as follow: For example, a, b and c are all random number from uniform distribution in certain range (different between each other). ...
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2answers
33 views

Analytical form of a joint PDF of two uniformly distributed random variables

I was wondering if it is possible to write down (closed-form analytically) the joint density function of two uniformly distributed random variables (X and Y, each on a closed interval dX=x2-x1 & ...
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26 views

How do you calculate randomness?

Suppose I receive a list of 1 million coinflips, and I want to know how likely it is that the list was randomly generated. My first thought would be to count the number of heads and tails, which ...
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1answer
46 views

Query relating to marginal pdf (probability density function)

I have a set of two related queries relating to marginal pdfs: i.How to proceed finding the marginal pdfs of two independent gamma distributions (X1 and X2) with parameters (α1,β) and (α2,β) ...
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Pictogram questions about statistics

This figure shows a graph taken from an advertisement for an investment that promises to pay a higher interest rate than bank accounts and other competing investments is this graph a correct ...
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What is suspicious here? (Statistics)

The late English psychologist Cyril Burt was known for his studies of the IQ scores of identical twins who were raised apart. The high correlation between the IQs of separated twins in Burt's studies ...
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3answers
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Probability of drawing certain hand, incorrect answer, but why? [duplicate]

So I am drawing $5$ cards from a standard deck of $52%$ I want to find the probability that I draw $5$ consecutive cards of same suit with no card looping, and the ace is card $1$. So the ...
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2answers
26 views

Counting Number of Possibilities using Inclusion-Exclusion

I have been tasked with answering the following combinatorics problem for a homework assignment: Consider the set of all six digit numbers that don’t begin with 0. How many of these have at least one ...
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How many Mad Libs combinations will result when requiring a particular distance between sentences?

You are randomly filling in a Mad Libs type sentence with words from a set of dictionaries. For instance: Sentence: The [COLOR] [ANIMAL] [VERBED] a [NOUN]. Dictionaries: COLOR: blue white orange ...
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is it a classical statistical question?

Assume a box of balls whose total number is N. Each ball is with a specific value on it. The distribution of these values are known. Give a specific value x. Now we draw n balls from the box each time ...
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Let $X$ be a random variable with mean 2 and variance 1. Find the mean of $Y = 4X + 10$ [closed]

What's the procedure to answer this? I'm not sure where to start.
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2answers
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Expected Total Number

To determine whether or not they have a certain disease, 160 people are to have their blood tested. However, rather than testing each individual separately, it has been decided first to group the ...
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1answer
22 views

Let X be a discrete random variable

Let X be a discrete random variable. If $E[X]=-3$, then $E[(3+5X)^2]=$ I understand that to find the expected value the formula would be $E[aX+b] = aE[X]+b$ so it would be 3+5(-3). My problem is ...
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1answer
22 views

Point estimators

I hope someone can point me in the right direction with this: If I have $X(1), X(2), X(3), X(4)$ taken from a population with a mean $\mu$ and a variance $\sigma^2$, how do I show that $\hat \mu= ...
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1answer
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Probability questions (independent events)

Three people are going to a dinner. the probability that Albertine, Karoline and Patronelle is going is 0.8,0.6,0.9 respectively. a) what is the probability all 3 are going? is this just ...
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1answer
12 views

Finding pooled variance

Find the variance of $S^2_p$ under the conditions; $\bar{x_1}, \bar{x_2}, s_1, s_2$ are the means and standard deviations of independent random samples of sizes $n_1$ and $n_2$ from normal populations ...
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1answer
18 views

Finding a confidence interval

Given Distribution: $f(R) =\begin{cases} \frac{2}{\theta^2}(\theta-R), & \text{for } 0 <R<\theta \\[2ex] 0, & \text{elsewhere} \end{cases}$ Question: Find $c$ so that ...
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1answer
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Cumulative Distribution Function applied to exponential variables

Let P be a program composed by two sub-programs that have execution time of T1 and T2 distributed with exponential law of parameters u1 and u2. I have to calculate the Cumulative Distribution ...
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Proving $Corr(\hat{e}_{ij}, \hat{e}_{jk}) = \frac{-1}{n_i-1}$ for $ j \neq k$

For the model of a single factor experiment: $y_{ij}= \mu + \alpha_i + e_{ij}$, $(1 \leq i \leq a, 1 \leq j \leq n_i)$, where a = the number of treatments, $n_i$ = the number of experimental units ...