# 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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### What is the probability that $X \geq k\cdot Y$, if X and Y are independent and follow the exponential distribution?

$X$ and $Y$ are independent variables that follow the exponential distribution with the same parameter $\beta$. What is the probability $$P(X \geq k\cdot Y)$$ if $k>0$ ? I don't really know where ...
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### How do I compare rates of error between two different sample sizes?

I'm unsure on how to normalize for two different variables. Person A makes 20 pastries total, whereas Person B makes 50. 5 of those pastries, so 25%, are sampled from Person A; 10 for Person B, for ...
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### Variance of exponential moving average

I'm not quite sure what the form for the rolling recursive variance should look like. I have that the recursive average is $m_t = \alpha x_t +(1-a)m_{t-1}$. Then would the rolling recursive variance ...
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### Which Statistical method should I use? [migrated]

I have been given a problem and need to find the best statistical method that would help. The problem is as follows: A business has approx. 100,000 active customers who spend between £500 per annum ...
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### Show that $n \to \infty, \sqrt{n}(Y_{n}-p) \rightarrow N(0,p(1-p)$

Can anyone show me the correct working out to find the variance for $Y_n$, My variance seems to be $\frac{p(1-p)}{n}$
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### What test to use? [closed]

For my AP Statistics final, my teacher had our class do a research project where we collect data of our own intetesting subject and then present our findings. I did a response semi-survey thing using ...
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### Question about Moment generating functions, precision, rounding errors

Hello I have a question in regard to moment generating functions and something I noticed but wasnt to clear on. Say that a random variable $X$ has $$MGF=M_{X}(t)=\frac{4}{4-t^2}$$ for $-2 \lt t \lt 2$...
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### I am getting asteriks in minitab for the p--value when i try to do a Two-Way ANOVA

I am trying to do a Two-Way ANOVA. I did what i think I need to do to have the p-value show up on the screen (after i click the button that starts the calculation) but, all i see next to the P-value ...
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### Finding a unique point in a histogram that can be determined even if the histogram is circularly shifted.

Circularly shifted histogram: Modular addition (or subtraction) of a constant value to all data points. Maxima, Minima, etc. might not be a unique value, therefore can't be used. Edit: Let me ...
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### Sigma Sum Properties

My Probability and Statistics teacher wrote the following: http://imgur.com/z0rgylh How can I prove such step? Thank you very much!
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### Probability of basketball shots in a row

I've read some of the answer with this related question but it's not somewhat the answer I'm looking for. A player has a $75\%$ free throw percentage. Can someone explain to me why the probability of ...
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### Distribution table for number of white balls without replacement

I have a box with $4$ white and $2$ black balls. I want to find the random variable distribution table for the number of white balls when I take $3$ balls without replacement. Now if we had ...
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### coefficient of determination: absence of cross products [closed]

With regard to the coefficient of determination, why is the total variation equal to the sum of the explained variation and the unexplained variation and there are no cross-products?
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### Can we model this set of experiments as an stochastic process and estimate the sample size?

I have an image with the size 5575x9440 and I'm implementing a modified version of the algorithm used in this paper on it, but because the code performance is low ...
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### Finding the confidence interval of a normally distributed sample

Traffic police monitor the speed of vehicles as they travel over a new bridge. The average speed for a sample of 27 vehicles was 91.29 km/h, with the sample standard deviation being 4.94 km/h. We will ...
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### Probability of Detecting an Event Given No Previous Detections

I'm trying to figure out: Given a probability distribution of how likely an event is to be detected at time $t=1,t=2,t=3,t=4$ etc, what is the probability that it will be detected at t=n+1 if it is ...
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### Importance sampling example

I have a question regarding importance sampling. During a lecture we were told that importance sampling is simply a shift to another PDF to improve point sampling. I=\int_{a}^{b}dx\ f(...
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### Do we not have that $X_1, \ldots, X_n \sim F$ iff $X_1, \ldots, X_n \sim f$?

From pg. 39 of All of Statistics: If $X_1, \ldots, X_n$ are independent and each has the same marginal distribution CDF $F$, we say that $X_1, \ldots, X_n$ are IID (independent and identically ...
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### Best fit with unknown functional form

I have data from a simulation of a certain function $F(x)$ for a discrete set of values $\{x_i\}$. I know that $$F(x) = A \ f(x) + B \ g(x)$$ where $A,B$ are (real, positive) constants and $f,g$ ...
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### Comparing two observations with given significance level

My data is as follows: for each of French municipalities the mean income of inhabitants is given. My sets consists therefore of pairs (municipality, mean income). I am asked to compare two ...
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### Integration Question Arising from Attempting to Compute a Marginal Distribution

I have a question about the last step of a proof on page 37 of All of Statistics. The entire proof is here for sake of completeness, but I don't think grokking it in its entirety is necessary for ...
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