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Questions tagged [statistics]

Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory and other branches of mathematics such as linear algebra and analysis.

Statistics is the science of the collection, organization, and interpretation of data. It deals with many aspects of data, which includes the planning of data collection in terms of the design of surveys and experiments. (From Wikipedia)

More specifically, 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 mathematical analysis. (From Wikipedia)

For questions which are more generally about collecting and treating data, it is advised that you post your question on Cross Validated and DSSE.

37109 questions
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Pooled Estimate of the Variance

Suppose $X_{1},\dots,X_{m}$ is iid $N(\mu_{1},\sigma^{2})$ and $Y_{1},\dots,Y_{n}$ is iid $N(\mu_{2},\sigma^{2})$. Is it true that the pooled estimate of the variance, $S_{p}^{2}$, has the property…
Kirk Fogg
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Binomial Probability question!!!

A card is drawn and replaced five times from an ordinary deck of $52$ cards and the sequence of colors is observed. What is the probability that: a) Five red cards were drawn? b) five black cards were drawn? c) Three red and two black cards were…
user85956
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Find $c$ for $P(\frac{5}{12}-c \le Y \le \frac{5}{12}+c)=\frac{1}{2}$

Find $c$ for $P(\frac{5}{12}-c \le Y \le \frac{5}{12}+c)=\frac{1}{2}$ We also have that $$f_Y(y) = k\sum_{i=0}^{\infty}y^i, y\in(1/3, 1/2) \\ \implies k\int_{1/3}^{1/2}\frac{1}{1-y}dy \implies k=\frac{1}{\log(\frac{4}{3})}$$ What I have tried: I had…
Working dollar
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Probability of two things combined larger than probability of one of them?

I am going through a course on basic statistics and instructor presented a problem, with a solution. To me it looks like the problem does not have a solution at all, let alone the solution posted by instructor. Most likely I am wrong, could you…
Artem Lebedev
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Covariance of transformed random variable

So I have the covariance $\mathsf{cov}(x_0,x_1)$ and I know $m_b=−2.5\log_{10}(x_0)+$constant, then how do I calculate $\mathsf{cov}(m_b,x_1)$ I found this but I guess it isn't useful here since it is transformation of both the variables. Also i…
SHIN101
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Sufficient Statistic for exponential family

Let $\mu, \nu$ be positive and suppose that $X_1,...,X_n$ are exponential with parameter $\mu$, and $Y_1,...,Y_m$ are exponential with paramter $\nu$ and that all variables are independent. Construct the generalized likelihood ratio test for the…
Math_Day
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Are there any problem books with solutions for an elementary business statistic course?

As my teacher doesn't use any textbooks in the course, I can only depend on the exercises that were given to me. The main reference textbook (which is never discussed at all) that I have for my course doesn't have any solutions in it therefore I can…
Dixon
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Relation between normal distribution and binomial distribution to calculate number of individuals

We let be the weight of a random potato from Maria's kitchen garden. We assume that is normally distributed with an mean of 200 grams and a standard deviation of 40 grams. Maria will pick up potatoes. She picks a random potato from the kitchen…
F.O
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Bar chart or histogram

What's the difference between a bar chart and a histogram?
Jimmy
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pdf of $\frac{(X_1-X_2)^2}{2}$

Let $X_1$ and $X_2$ be independent normally distributed random variables. $$X_1 \sim N(0,1) \\ X_2 \sim N(0,1)$$ Find the pdf of $\frac{(X_1-X_2)^2}{2}$ We have that By example we know that when $Y = X^2$ we have that $$\begin{align}f_Y(y) &=…
dollar bill
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How do I calculate the average length (value) of a subscription given monthly retention rates?

For instance, imagine I have two subscription offerings. One is monthly at \$5. The other is yearly at \$50. I want to know "is a user who subscribes monthly likely to generate more lifetime revenue than a user who subscribers yearly"? The results…
christianselig
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About Copulas , Im not sure it true or false

In Copulas, If $C(F(x) , G(y)) = \min (F(x) , G(y))$ then $F(x) = G(y)$. Is it true or false? Thanks.
Doretomtom
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probability problem

3 machines (a1,a2,a3) produce parts a1=45% a2=35% a3=20% 10% of a1 are defective 6% of a2 is defecyive 2% of a3 is defective a)prob of a random part chosen to not be defective b)part produced by a1 a) i thought of finding the defective first then…
spiros
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excel-distribution function

I have an exercise in statistics in witch I need to generate n values ​​of a random variable X having the distribution function F ( in excel ). I don't understand how I should do that in excel.
user981656
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Comparing a %increase with a %decrease

I'm struggling to compare the %increase/decrease in the average homicide rate of a select group of cities to the state homicide rate. For example, if the state saw a 4% decrease (-4) in the homicide rate over a two-year period but the average…
Brittany Nieto
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