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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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
15 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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2answers
32 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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0answers
7 views

A joint pdf question

I need help over a question. I appreciate all helps.Thank you.
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1answer
10 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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0answers
5 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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0answers
10 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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0answers
15 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
14 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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0answers
5 views

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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0answers
6 views

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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0answers
11 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 ...
3
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2answers
21 views

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
19 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 ...
1
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0answers
26 views

Mutual Exclusivity

Suppose that a study is being done on all families with one, two, or three children. Let the outcomes of the study be the genders of the children in descending order of their age. A. List sample ...
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0answers
13 views

A linear algebra textbook that is advanced enough as a prerequisite to read time series and econometric textbook?

A linear algebra textbook that is advanced and comprehensive enough as a prerequisite to read time series by Hamiliton and econometric by Hayashi? If possible, please also answer on which statistics ...
2
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1answer
24 views

Why does β=α give a symmetric standard beta pdf?

I know that β=α is what will give a symmetric standard beta pdf, but why is this so?
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0answers
10 views

Finding the distribution of $\bar{Y}_{1+} - \bar{Y}_{2+}$ in randomized block design

Please help me, I've been stuck on this problem for so long! I'm trying to find the distribution of the following but I am having quite a hard time as Mathematics/Statistics has always been difficult ...
1
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0answers
21 views

Negative Correlation and Securities?

The following is a problem in the textbook I am trying to do as I practice for an exam. I would appreciate some help on this question I have completed part a. I have determined expected return in ...
2
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0answers
12 views

How to compute uniformly distributed points on an ellipse

The ellipse can be parametrized in polar coordinates by $$r(\theta)=\frac{1}{a+\cos\theta}$$ up to a scaling factor, and $a>1$. Suppose we measure $S$, the distance along the ellipse from the ...
2
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2answers
20 views

Covariance for equal variances

If X and Y are independent random variables with equal variances, find Cov(X+Y, X-Y). I am confused on how to do this? I feel like I am over thinking this question.
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0answers
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orderstatistics of uniform distributions on different ranges

During a simulation I discovered an interesting phenomenon: Given you have 3 agents. 2 are uniformly distributed between [0,1] and one between [0,2]. The question is how often do the smaller agents ...
0
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0answers
11 views

normal distribution

An urn contains 8 green balls and 17 yellow balls. A ball is drawn from the urn, its colour is noted, and then the ball is placed back in the urn; 15 balls are drawn in this fashion. (a) Would it be ...
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2answers
10 views

Variance & Joint Density Function

$X$ and $Y$ have joint density given by $$f_{XY}(x,y)=\begin{cases}2,& 0≤x≤y≤1 \\0,& \text{elsewhere}\end{cases}$$ a) Find $\text{Var}(Y|X=x_0)$. b) What is the answer if $x_0$ is not in the ...
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1answer
12 views

approximations of discrete distributions

if X is b(100,0.1), find the approximate value of P(12<=X<=14),using a) The normal approximation b) The Poisson approximation c) The binominal using the binominal approximation I think it ...
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3answers
32 views

P(A|B^c) given the following

Given $P(A) = 0.2, P(B) = 0.6$, where A and B are mutually exclusive, find the conditional probability $P(A|B^c)$. How do I determine this answer? I've been trying to figure it out for hours.
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0answers
2 views

Best Estimate for Mean Difference

To compare two methods for the determination of uric acid, 23 blood samples from 23 individuals were divided and analyzed both by the colorimetric method and the uricase method. Suppose the sample ...
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0answers
16 views

What makes standard deviation a good measure of dispersion from the mean?

Standard deviation formula: If I just want to measure the amount of dispersion from the mean, why can't it be just an average of the absolute differences of each term from the mean? Something like ...
0
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1answer
19 views

asymptotic series for “stable distribution”

I'm trying to understand how to get from one equation to another in a certain paper I am studying (DOI:10.1080/00018738100101467, eqs. 4.34 and 4.35). The equations are pretty self contained, so I'm ...
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0answers
6 views

How to calculate probabilities of win, draw and loss based on the ELO system

Consider one game between two opponents (I am actually thinking about chess but it doesn't have to be that). The ELO rating system gives the expected score $E_A$ and $E_B$ for both players. That is ...
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0answers
9 views

Negative binomial distribution's mgf!

I've got problem. during my trying to find mgf(moment generating function) of negative binomial distribution, I found myself cannot understanding process. How does second line become third line? ...
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1answer
22 views

Infinite boundary for random variables

I have a question Suppose that X and Y are random variables with joint pdf is given by and zero otherwise. I need to find marginal and conditional pdf's.But I don't know how to intagrate over an ...
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1answer
41 views

Probability question - statistics

 Could somebody please help me, I have been trying to calculate this problem all day, but with no success. Here is the problem: "A teacher was asked by her principal to select 7 students at random ...
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1answer
32 views
-3
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1answer
55 views

A baseball player's batting average is $0.31$. If, in a given game, [on hold]

he bats four times, what is the probability that he will get: no hits? at most two hits? at least two hits?
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0answers
33 views

If $Y=X\beta+\epsilon$, prove that the least square estimator $\hat\beta$ is independent of $Y-X\hat{\beta}$

Let $Y=X\beta+\epsilon$, where $Y$ is an $n$ by $1$ vector, $X$ is an $n$ by $p$ matrix with full rank and $\epsilon$ is an $n$ by 1 vector of random errors independently and normally distribution ...
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0answers
58 views

Probability question in statistics [on hold]

Suppose I give you a list of 24 problems to study, from which I will randomly pick 14 questions for your first midterm exam. For whatever reason, you prepare for the midterm exam by completing and ...
-1
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0answers
29 views

stochastic model [on hold]

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
35 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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1answer
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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votes
1answer
30 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 ...
2
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0answers
26 views

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? ...
0
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0answers
20 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 ...
-1
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0answers
11 views

Assigning a numerical value to clarity [on hold]

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 ...
1
vote
1answer
33 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. ...
0
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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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0answers
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 ...
1
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2answers
20 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 ...
0
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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 ...
0
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1answer
31 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 ...