# 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.

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### Uniformly Distributed Random Variables Minimum

Let A,B,C,D,E be independent random variables, each of which is uniformly distributed in the interval [0,18]. Let X=min{A,B,C,D,E}. What is the expected value of X? Enter your answer as a decimal. ...
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### Find a 99% confidence interval for the population mean for a sample of size 36 that yields a mean of 78 and a standard deviation of 6…

Find a 99% confidence interval for the population mean for a sample of size 36 that yields a mean of 78 and a standard deviation of 6. Assume sigma, the population standard deviation, is unknown. A) (...
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### Proving Unbiased estimators

Hello all, Here is a question I am struggling to understand, ...
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### Determining how accurate an ellipse fit is

So I have an image of bacteria particles which are often shaped very irregularly with many grooves. Im trying to fit ellipses onto these particles so I can get a better, more smooth analysis of the ...
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### How to know when samples tend toward lowest number?

I am working on a computer simulation. In a perfect world, I only want to know what the minimum result value is from the simulation. (I have no a-priori knowledge about the range of numbers or their ...
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### The golden ratio in statistics of literature

Let a book, for example, or a poem... It consists in words and letters and symbols like : ;,!... Let $W_b$=the number of words of the book. Let $L_b$=the number of letters of the book. The number $N_b$...
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### Hypothesis testing using chi-square distribbution

Four players meet weekly and play eight hands of cards. Over a year, one of the payers finds that he has won x of the eight hands with frequency fx given in the following table: x 0 1 2 3 4 5 6 7 8 ...
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### Green balls and Red balls, probability problem

I'm studying for my exam and I came across the following draw without replacement problem : ...
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### Why does $E[X]$ not equal the integral of $f(x)^2$

If $X$ is a random variable with the pdf $f(x)$ and $Y=g(X)$ how come $E[Y]$ is the integral of $g(x)f(x)$ but $E[X]$ is the intergral of $xf(x)$ ??
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### What's the MLE of lambda for $f(x)= \frac{1}{λ}\exp{\frac{−x}{λ}}$?

What's the MLE of $\lambda$ for $$f(x)= \frac{1}{λ}\exp\left({\frac{−x}{λ}}\right)$$ Values of x are 5,7,9,3,6,8 Is it just the mean of $x$? Thanks.
Suppose $P(X_{n}=i) = \frac{n+i}{3n+3},$ for $i = 0, 1, 2$. Find the limiting distribution of $X_{n}$. Is the cdf $F_{x_{n}}$ like: " if x = 0, $F_{x_{n}} = \frac{n}{3n+3}$; if x = 1, $F_{x_{n}} = ... 3answers 52 views ### Conditional probability - finding a single event Context:$P(L) = 0.1$,$P(M | L) = 0.45, P(M | L') = 0.51M =$Male,$M' =$Female,$L =$Left handed,$L' =$Right handed. 1. Find$P(M)$. So I knew I had$P(M | L)$and$P(M | L')$so I ... 1answer 111 views ### Coefficient of variation - Help me decode this text Doing some exercises I hit upon this wall of text: Coefficient of Variation should only be computed on ratio scales (i.e., data where there is a "true" zero, like temperatures in Kelvin, or ... 1answer 113 views ### Standard Deviation and Mean take a look at this question: The sample from Population A has a mean of 35 and a standard deviation of 1. The sample from Population B has a mean of 45 and a standard deviation of 15. Which of ... 0answers 41 views ### Randomized Block Design for repeated trials - Please help Suppose I measure reaction time of 4 students, initially before any treatment, then after treatment 1, and finally after treatment 2. (Note all treatments will eventually be applied to all students) ... 1answer 60 views ### Question on finding the Jacobian I have a question which is as follows: The random variable U has the pdf$n \dfrac{u^{n-1}}{\theta^{n}}$,$ 0 \le u \le \theta$This is not independent of the parameter θ. Let Y=U/θ. Use the ... 1answer 36 views ### some knowledge about comare means of two group I'm studying a bout statistic. I can compute very well. But i don't really know well. I want to know clearly about theory. And i have this problem: An experimenter wishes to compare two ... 2answers 45 views ### stats - limiting distribution Let$0 < p < 1$, and let$X_{n}$have p.d.f.$f_{n}(x) = ( 1 – p ) ( n + 1 ) ( 1 – x )^{n} + p n x^{n – 1}$, for 0 < x < 1, zero elsewhere. Find the limiting distribution of$X_{n}$. ... 1answer 202 views ### Prove that$COV(h(x),g(x)) \leq 0$means the different direction for$h,g$(Covariance Inequality) Prove that if$g$is nondecreasing and$h$nonincreasing, then $$E(g(X)h(X)) \leq E(g(X)) E(h(X))$$ I know that it is equivallent to prove$COV(g(X),h(X)) \leq 0$if$h$... 1answer 109 views ### Probability: 30 balls in a bucket, homework i need some help with some homework, first time i am doing probability and statistics, id like to know if my 2 answers below are correct, and how i can solve the remaining 2. There are 30 balls in a ... 1answer 65 views ### stats - determine limiting distribution Let$Y_{1} < Y_{2} < ... < Y_{n}$be the order statistics of a random sample from a distribution with pdf$f(x) = e^{-x} , 0 < x < \infty$, zero elsewhere. Determine the limiting ... 0answers 56 views ### Order statistics of random variables Let$\{I_1, I_2, \dotsc, I_N\}$be$N$i.i.d random variables. I know that the smallest orders statistics and the largest one are defined respectively as follow: $$I_{(1)}=\min(\{I_1, I_2, \dotsc, ... 2answers 49 views ### What is this pattern? I have a pattern of numbers from some simulation that I'm trying to piece backwards into some sort of formula. All I can see right now is that they maybe have to do with integrals? The numbers (which ... 0answers 115 views ### Combining confidence intervals for sums of generic random variables So my fiancee is a civil servant and asked me for help with the following problem. She has been given a collection of upper and lower bounds on expenditure for a collection of projects like: ... 1answer 100 views ### How to choice between paired sample and Independent sample I don't know how to decide to choose between pair and Independent to compare mean of two groups. Here is the excersise from a book: ... 1answer 113 views ### Fishers Exact test alternative to chi-squared? Background*strong text* Am analysing results from a questionnaire (n=130). The respondents fall into four categories (A / B / C / D), and each question/statement has 5 possible answers (Likert Scale ... 1answer 17 views ### Combining Random Variables to get the Variance So$$\operatorname{Var}(aX + bY) = a^2 \operatorname{Var}(X) + b^2 \operatorname{Var}(Y).$$But I have also seen:$$\operatorname{Var}(aX - bY) = a \operatorname{Var}(X) + b \operatorname{Var}(Y).$$... 1answer 82 views ### Find an unbiased estimator Let$X$be an r.v defined by$P(X=0)=p$and$P(X=1)=1-p$. Find an unbiased estimator for$2p$. My solution:$E(X)=1-p$so$2-2E(X)$is unbiased. Is this correct? 1answer 159 views ### Expectation by conditioning Problem: Independent trials, each of which is a success with probability$p$, are performed until there are$k$consecutive successes. What is the mean number of necessary trials? Start on solution. ... 1answer 103 views ### Confidence interval for n=1, unknown standard deviation Is there any way to calculate a confidence interval (or otherwise gauge the reliability of a sample) when you have a sample size of one and you don't know the population standard deviation? I work at ... 2answers 1k views ### Meaning of covariance Can someone please give me an intuitive explanation for the meaning of covariance between two random variables? What does it measure?! 1answer 2k views ### Upper and Lower Bounds for Confidence Intervals on a one tail hypothesis test. CI(99) = xbar ± Zcv( σ / √ n -1 ) My question is if the test is a one tail hypothesis test, do I still do two separate equations + and -. Here is the formula filled in (if it is the correct formula)... 1answer 15 views ### Why am I getting 84.25 instead of 97.68 for my Confidence Interval? Why am I getting 84.25. I am doing 97.96*(6/sqrt[50-1]) = 97.96*(6/7) I am obviously not doing this correctly please help. It has been sometime since I have done any math. 1answer 44 views ### statistical significance in non normal distributed data I have randomized strings undergoing two different tests. There's a pretty clear difference in their proportions, but it reminded me of apstats where you would often do 2prop Z-tests to compare to ... 1answer 83 views ### Expected Value of a function of the standard normal distribution Any help is appreciated. Thanks 1answer 40 views ### Covariance Problem I'm trying to find the solution to$cov(y_i, \frac{\sum{y_i}}{n})$, where$y_i = \beta_0 + \beta_1x_i + \epsilon_i$(a regression model). Here's what I have so far...$cov(y_i, \frac{\sum{y_i}}{n}) ...
Suppose I have $X$ and $Y$ as random variables and have their joint probability distributions. Is the following correct: $f_{X,Y}(x,y) = f_{Y,X}(y,x)$ ?