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

0
votes
1answer
47 views

What is a “moment” in mathematics, and what does it mean?

This is a general question. I would like a better conceptual understanding of what a moment is, it's meaning, and it's applications (not just in probability). I already looked at Wikipedia, but I ...
0
votes
2answers
32 views

How do I find the $Z$ value and calculate the $P$?

Please DO NOT answer the question, as I just need the right formulas in the form of plugging the numbers from the word problem into it. I struggle with this. And I need to find what the percentage is ...
0
votes
1answer
53 views

Problem calculating the probability that the mean score is less than a certain value.

I'm quite new to statistics and I'm having some trouble solving this problem: An unbiased dice is thrown $70$ times. Find the probability that the mean score is less than $3.3$. Here's what I ...
0
votes
1answer
40 views

Probability density function: what's a measure $X_*P$?

The Wikipedia article on PDFs defines the probability distribution of a random variable $X$ in $(\mathcal{X},\mathcal{A})$ to be the measure $X_*P$ on $(\mathcal{X},\mathcal{A})$. I understand what a ...
0
votes
1answer
42 views

Wald Test Statistic

I am trying to understand the Wald test statistic as explained at https://en.wikipedia.org/wiki/Wald_test . What I do not understand is the parameter R in the test statistic: H0: R*theta = r I ...
0
votes
2answers
81 views

Using the Law of Total Probability to Show

I'm really struggling with understanding how to use the Law of Total Probability in proof questions such as this one. Any help would be hugely appreciated. The number of emails received in a day has ...
0
votes
1answer
41 views

Finding $P(X+Y=10)$ when $X$ and $Y$ are both of geometric distribution

I am having difficulty finding $P(X+Y=10)$, given that $X$ and $Y$ are independent and both are geometrically distributed: $$P(X=k)=P(Y=k)=p^k(1-p), \ \ \ k=0,1,2,...$$ I attempted to set $X=10-Y$ ...
0
votes
1answer
60 views

Finding the marginal probability function of…

The random number Y has a Poisson distribution with the parameter x. However, x itself is a random variable with the probability density function given by: $$f(x) = \begin{cases}e^{-x} &\text{ ...
0
votes
2answers
63 views

Find $P(Y_1≤3/4,Y_2≥1/2)$ of a joint probability density function.

Let Y1 and Y2 have the joint probability density function given by: $ f (y_1, y_2) = 6(1−y_2), \text{for } 0≤y_1 ≤y_2 ≤1$ Find $P(Y_1≤3/4,Y_2≥1/2).$ Answer: $$\int_{1/2}^{3/4}\int_{y_1}^{1}6(1− ...
0
votes
1answer
46 views

What is P(Y1−Y2>3) of a given joint density function?

Let $Y_1 $and $Y_2$ have joint density function: $$f (y_1, y_2) = e^{-(y_1+y_2)}, \text{for all } y_1 >0,y_2 >0 $$ What is $P(Y_1−Y_2>3)$? My attempt: $$P(Y_1−Y_2>3) = P(Y_1−3> Y_2)$...
0
votes
1answer
22 views

Hypothesis Testing Using Critical Values

If my data $X_i\sim N(\mu,σ^2)$ is iid with a sample $n=35$ If my 99% confidence interval is $[.56,1.86]$ where $P(t>2.7238)=.005$ for a $t(34)$ random variable $t$ How would I derive $\bar{X}$ ...
0
votes
2answers
67 views

Probability theory question about trains and it schedule

I received some question for my exam preparation, but I'm not sure about the answer. So I need some reasonable explanation of the following tasks: I. Every day Sonja arrives at the railway station ...
0
votes
1answer
138 views

Probability. 100 questions with 4 answers.

I'm currently trying to solve this probability question and I'm quite unsure if my answer is correct or not. On a multiple-choice exam, there are $100$ questions each with $4$ possible choices. A ...
0
votes
2answers
19 views

Show that Covariance is $0$

Given this pdf: $$f(y_1,y_2)=\begin{cases} 4y_1y_2 & 0\leq y_1\leq1 \\ 0 & \text{otherwise} \\ \end{cases} $$ The goal is to show that $\text{Cov}(Y_1,Y_2) = 0$. First I ...
0
votes
2answers
65 views

Probability question regarding binomial distribution

I'm doing some work on the binomial distribution but currently finding it difficult to know whether my attempt of the question is the actual correct way to do it? At a party, it is discovered that ...
0
votes
1answer
35 views

an urn containing 5 green and 2 red balls

An urn contains 5 green and 2 red balls. One ball is drawn at random and its colour is recorded. This selected ball is then replaced in the urn and 3 more balls of the same colour are added to the urn....
0
votes
2answers
54 views

High school Math: Finding the Median

I have a problem trying to understand the following two questions: In question 1, the median is found at the 50% of the total group. However, this strategy doesn't work for question 2. Why?
0
votes
1answer
131 views

Show that 2Y/θ has a chi-square distribution

The question is Let Y be a random variable with a Gamma distribution with parameters α > 0 and θ > 0. Show that 2Y/θ has a chi-square distribution. What is the number of degrees of freedom? I am ...
0
votes
1answer
43 views

Which random variable has the characteristic function $f(t)=\frac{e^{it}}{1-it}$

Which random variable has the characteristic function $$f(t)=\frac{e^{it}}{1-it}$$ This is quite important for me to know, I know I have seen it somewhere, but I cant remember which random variable.
0
votes
2answers
33 views

Econometrics Conditional Mean

I have a question regarding linear regression. Suppose we have the following regression model: $$ y_{it}=\alpha+x_{it}'\beta+u_{it} $$ where say $i$ represents individual $i$ at time period $t.$ The ...
0
votes
2answers
33 views

Get c.d.f. from given p.d.f.

The p.d.f. for $X$ is: $$f_X(x) = \begin{cases} \frac{1}{18}(x+3) & -3 < x < 0 \\ \frac{1}{54}(9-x) & 0\leq x < 9 \\ 0 & otherwise \end{cases}$$ I found the c.d....
0
votes
1answer
44 views

Calculate sample variance from tallied data

How friends, I am studying Statitics on my own and I am looking for someone to promp me to understand how to approach questions of this nature. I am used to frequency tables but not this one. The ...
0
votes
1answer
148 views

Probability of an unbalanced coin

This was an optional practice problem in statistics: An unbalanced coin has a 0.3 probability of being heads. The coin is tossed 20 times, let Y be the number of heads recorded. a) Find the ...
0
votes
1answer
46 views

Find the density of the random variable $Y=X^2$

Find the density of the random variable $Y = X^2$, if the random variable $X$ follows a standard normal distribution. I think I should use mgf to solve it is that right ? what should I do to start ?
0
votes
2answers
32 views

Probability: Flipping a Coin

I have an extra credit problem for my statistics class that I am stuck on, thanks in advance for the help! If you flip a coin four times, letting x be the number of tails then find the probability of ...
0
votes
2answers
131 views

Find the probability that a prime number of dots appear in the first throw

A fair dice is thrown twice. Find the probability that a prime number of dots appear in the first throw and the number of dots in second is less than 5 I am not too sure how to approach this one, any ...
0
votes
1answer
22 views

Prove the following equality to show a relationship between Poisson and Gamma Random Variables

I've been trying to do integration by parts on the following left side of this equation for the past half hour but my problem is that I cannot get rid of the Gamma variable. For the left side, I see ...
0
votes
2answers
112 views

distribution flip a coin 1000 times

If a coin is flipped 1000 times, 600 are heads, would you say it's fair? My first thought was to calculate the p-value. Assume it's fair, the probability of getting 600 or more heads will be ...
0
votes
1answer
18 views

If $X$ is binomial$(n,p)$, find unbiased estimator for $p^2$

So I know I'm looking to find a function $\delta(X)$ so that $E\left[\delta(X)\right] = p^2$. Let me venture a guess that $\delta = \hat{p}^2 = \frac{x^2}{n^2}$. Then: $$E\left[\hat{p}^2 \right] = E\...
0
votes
1answer
37 views

Total accumulated risk

I'm a big fan of Minesweeper. Like other fans, I know that probabilities are important in this game. So, for more fun, I play on this player : http://mrgris.com/projects/minesweepr/demo/player/. ...
0
votes
2answers
407 views

Prove that the Expected value of Y bar ^2 = µ^2

I'm trying to show whether or not $\bar(Y^2)$ = $\\µ^2$ Or the mean of the sample squared) is a biased or unbiased estimator of the population mean squared. I can prove that Ybar is an unbiased ...
0
votes
1answer
26 views

Upper bound on an expectation

I'm looking for an upper bound on $E(X^k)$ where $X$ is a random variable with $E(X)=1$. How can I go about doing this?
0
votes
2answers
39 views

Drawing balls from a box based on die toss

Two boxes, the first contains 3 red & 2 white balls. The second box contains 4 red & 7 white balls. A fair die is tossed. If the outcome is even, a ball is drawn from the first box, while a ...
0
votes
1answer
29 views

Help: Setting a Discrete Joint table.

My first question is: If i did correctly the next table. For later calculate the asking probabilities.Thanks, again. I follow the advise of kitman0804, and I worked in build the correct table, here ...
0
votes
1answer
27 views

Need way to statistic puzzle

Hello guys i need help with statistic problem. The problem is : In room have 3 doors, one door is exit from room (o minutes) , second is return us to the room after 3 minutes , and last door is ...
0
votes
3answers
41 views

How to calculate the expected value on this example, part b, only.

A girl scout troup has 100 boxes of cookies to sell. Of these 100 boxes 60 are chocolate chip and 40 are sugar cookies. 10 boxes are randomly selected to be sold at a fair. (a) What is the ...
0
votes
2answers
63 views

Sum of N (N ~Geo) exponentially distributed random variables is exponentially distributed

Let $T_i$ for $i=1,2,...$ be a sequence of i.i.d exponential random variables with common parameter $\lambda$. Let $N$ be a geometric random variable with parameter $(1/(p+1))$ that is independent ...
0
votes
2answers
28 views

Probability and Expected Value as it approaches zero

I'm having issues understanding how to approach this question. Let $X_1, X_2, ... X_n$ be random variables in $(0,1)$ over some distribution. Prove that the following are equivalent. $\forall \...
0
votes
1answer
28 views

maximum and minimum distributions

Suppose that X is uniformly distributed on the interval [0,10] and suppose that Y=2X. Note that X is uniformly distributed on the interval of [0,20] Find the probability that min(X,20-Y)>7 What I ...
0
votes
1answer
56 views

How to show that $E[\hat\sigma^2_x]= \sigma^2_x$?

Suppose you want to estimate $\sigma^2_x$, the variance of a random variable $X$. We want to study the properties of a couple of estimators for the variance. You have an iid sample of $n$ observations....
0
votes
2answers
28 views

Why take the logarithm of likelihood function when finding MLE

To calculate the MLE, I see that we can easily take the logarithm of the likelihood function like so: https://en.wikipedia.org/wiki/Exponential_distribution#Maximum_likelihood I have the following ...
0
votes
2answers
27 views

How to understand this multiple regression question without having an example in the textbook?

How to understand this multiple regression question without having an example in the textbook? Please briefly show how to do the final question and give the answer to the final question.
0
votes
1answer
65 views

Estimate an error using method similar to Stirling's approximation?

In the application of WLLN, which is the polynomial approximation. For any function $F\in C([0,1])$ can be approximated by a polynomail $G$ so as to make $||F-G||=\max_{0\le x \le 1}F(x)-G(x)$ as ...
0
votes
1answer
75 views

matching problem - find variance using indicator variables

The question I am trying to solve is finding the $\mathsf E(X^2)$ in the matching problem (Let $X$ be the total number of matches if there are $n$ letters and $n$ envelopes randomly matched, etc). I ...
0
votes
2answers
27 views

Name for the operation $v \cdot M \cdot {v^T}$

Just wondering if there is a name for the operation of multiplying 1xN vector by an NxN matrix and then by the transpose of the vector. My feeble memory says that such a name might exist, perhaps in ...
0
votes
2answers
40 views

Help with probability problem

I have to solve the following probability problem but I'm not sure how: An electronics store is supplied with computers by three factories. From factory A obtains 30% from factory B 20% and from ...
0
votes
2answers
40 views

covariance of 2 poisson RVs

Im trying to calculate the covariance of x & y. Heres what I am given: z1 and z2 are independent poisson random variables with parameters 3 for Z1 and 5 for Z2. x= (z1+z2) y=(z1-z2) I have ...
0
votes
1answer
295 views

How to test whether a subset is representative of a population?

Given that I have an entire population's data, I'm looking to see if a subset that I take is representative of the population, on average. I'm not choosing randomly, as I plan to pick each item ...
0
votes
2answers
85 views

What's the difference between MCMC and particle MCMC?

Markov chain Monte Carlo (MCMC) methods are a class of algorithms for sampling from a probability distribution based on constructing a Markov chain that has the desired distribution as its equilibrium ...
0
votes
2answers
41 views

If $x_i$ is from a random sample is $Var(\bar x \mid x_i)=0$?

If $x_i$ is from a random sample, is the conditional variance of the mean (or the sum of squares, really any statistic based on $x$) just treated as a constant? I saw this in a OLS variance of a ...