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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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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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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0answers
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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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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0answers
48 views

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
30 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
21 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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0answers
14 views

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
43 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
30 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
25 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
36 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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0answers
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
47 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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2answers
21 views

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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21 views

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
36 views

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
27 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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0answers
22 views

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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27 views

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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3answers
100 views

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
43 views

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
40 views

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
14 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
25 views

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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0answers
9 views

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 ...
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1answer
31 views

Bayesian Network/ Number of parameters

Please consider the following Bayesian Network out of $Graphical Models in Applied Multivariate Statistics" by Joe Whittaker: Now the factorization property says that the joint probability ...
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1answer
27 views

poker hand: probability of getting 4 cards of equal face value and 1 card of a different value

A poker hand is defined as drawing 5 cards at random without replacement from a deck of 52 playing cards. Find the probability of the following poker hand: Four of a kind (4 cards of equals face value ...
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1answer
24 views

How would you explain this graph illustration of Simpson's paradox?

I need your help for understanding WHAT in the graph you find in the following link proves Simpson's Paradox. For those who don't know about Simpson's paradox, it is the inversion of the inequalities ...
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2answers
47 views

The inverse of AR structure correlation matrix / Kac-Murdock-Szeg ̈o matrix

I want to find the inverse of the following matrix: $$ R_{k-1}=\begin{pmatrix} 1 &\rho &\rho^2 &\cdots &\rho^{k-2} \\ \rho &1 &\rho &\cdots ...
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0answers
24 views

likelihood function of an exponential distribution using n and sample mean [on hold]

Let $x_1,..,x_n$ be a random sample (so that the corresponding $X_i$ are independent) from an exponential distribution with probability density function $f$(x|$\tau$)=$\frac1{\tau}$exp(-x/$\tau$) 0 ...
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0answers
11 views

Explanation of Gibrat Law

I read the article on wikipedia about Gibrat's law but it seems to be unclear. Basically it states that: The size of a firm and its growth rate are independent. Does it mean a small firm or a ...
1
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1answer
18 views

Normal distribution of independent and identically distributed variables

Suppose $X_1,...,X_n$ are independent and identically distributed $N(\mu,\sigma^2)$ random quantities. using the properties of independent normals and expectation and variance operators, explain why ...
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0answers
11 views

Generate a list of numbers based on range and quartile

I have the following requirement: A function to create a "list" container to hold a group of data with numValues data, and the range, median, and interquartile ranges ...
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0answers
31 views

Welford's algorithm for standard deviation: combine multiple sets of results

Suppose I use Welford's algorithm to compute the standard deviation of multiple sets of values. I only store all the n, mean and M2 results that the algorithm calculates, thus I have these three ...
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0answers
15 views

Square Root Transformation on a Random Variable

I read in my textbook that if Y ~ N(0,1) and Z is exponential with mean 1 (f(x) = exp(-x)), then X ~ sqrt(2Z)*Y follows a double exponential (Laplace) distribution with parameter 1 (f(x) = 1/2 ...
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1answer
10 views

Derivative-logarithmic equivalence

In working through a survival analysis textbook, I came across the following statement: $h(t) = \frac{-dS(t)/dt}{S(t)} $ is equivalent to $h(t) = \frac{-dlogS(t)}{d(t)} $ I can normally find my way ...
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1answer
60 views

Excel Problem-Correlation [closed]

A rich stock picker wants to decide between two stocks. One stock will pay a dividend of 100,000 its first year. After that, the dividend options look like this: a1=1, 1ST YEAR DIVIDEND + 30,000 ...
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1answer
24 views

Probability Mass Function, Variance, Expected Value [closed]

This was on a practice exam. I really need help with this question. I already completed 'a' and 'dii' Let X be a continuous random variable with probability density function f (x) = 2x, 0 ≤ x ≤ 1. ...
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1answer
20 views

Statistics help probalility

If boys and girls are equally likely to be born, what is the probability that in a randomly selected family of $4$ children, there will be at least one boy? (Find the answer using a formula. Round ...
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0answers
17 views

the Mahalanobis distance for 1D

I thought at the beginning that the Mahalanobis distance is only for more than or equal two variables until I found out a presentation for calculating the Mahalanobis distance for 1D. The formula is ...
2
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1answer
30 views

Probability of server cluster failure

I have a problem where I'm trying to derive an expression for the availability of a server cluster. Suppose I have 100 servers, where each one of them individually has a probability of failure 0.05. ...
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0answers
18 views

Probability Integral Transform of Discrete RV - Equating CDF's

If $F_X$ is the cdf of a discrete random variable X (with support of all integers) and $Y \sim $Uniform(0,1) such that $F_X^{-1}(y) = \mathrm{inf} \{x:F_X(x) \ge y\}$ (allow probability integral ...