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.
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If the mother group has $1000$ people with the female ratio of $30$%, how is it likely that a sample of $200$ could contain less than 5 females?
I believe the calculation would be like below:
$$
\dfrac{(1000-200)!200!}{1000!} \sum_{j=0}^5[\dfrac{300!}{(300-j)!j!} \cdot \dfrac{700!}{(700-200+j)!(200-j)!}]
$$
The first $\dfrac{(1000-200)!200!}{...
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Find Expectation and Variance of S and T and compare them.
Let, X~Bin(n,p) and Y~Poisson($\lambda$ ). Let
$$T=X_1+X_2+...+X_Y$$ with $X_i$'s i. i. d. Bin(n,p) (and independent to Y) and
$$S=Y_1+Y_2+...+Y_X$$ with $Y_i$'s i. i. d. Poisson($\lambda$) (and ...
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What is the difference between variance of estimate and estimated variance?
I am in a grad-level statistical inference class and literally getting all my concepts confused. Here's a cutout of the concepts that need most amount of clarifications: Rice Mathematical Statistics ...
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Does anyone know how to answer this stats q.?
Let $X$ and $Y$ be random variables with $E(Y) = 3$, $\operatorname{Var}(Y) = 4$, $E(X) = 5$, $\operatorname{Var}(X) = 6$, and $\operatorname{Cov}(X,Y) = 0$. Suppose we do a linear regression of $X$ ...
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P(X ≥ 10 and X is even)? - Stuck on probability question in Statistics
Question found here
I am currently stuck on this probability question for Intro to Stat. I have tried following the multiplication rule for probabilities by multiplying P(X is even) by P(X ≥ 10) and ...
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Stochastic Process Corollary
Anyone mind explaining what does this mean in layman terms? Does it mean the probability of variance of W is infinity is equal to 1? Thanks!
Let (W (t))t∈[0,T ] be a Wiener process. Then P(Var[0,T ] W ...
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Does there exist a $c: P(X<c)=2P(X>c)$
The proportion of impurities in a certain compound is a random variable with
density $f(x) = k x (1-x)$, where x belongs to $[0,2]$.
Calculate $k$.
Find the accumulated function.
Find $c$, a ...
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How to find variance for given problem?
Suppose the expected earnings for a farm depends on the number of worms per apple. The number of worms per apple has a Poisson distribution with mean 0.32.
a) The expected earnings per apple depends ...
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Probability of success in four free throws
I have the following problem:
There is a basketball player with a mean of success of $0.8$ per free throw. In a game, he has four free throws.
a) What is the probability of him succeeding in at least ...
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What is the first moment of ML estimator theta=n/sum(xi)
What is $$E\left[\frac{n}{\sum_i^nx_{i}}\right]$$
where $X_i\sim N\Big(\frac{1}{\theta}, 1\Big)$
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Asian option payout
How can I calculate the payout of an Asian option? I would like to know how to solve the mean over the entire lifetime of the option. Please show me how to calculate the following formula with the ...
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What's the answer to part (c)?
I only have trouble with part (c). For part (a), the answer is 0.0107 and for (b), the answer is 0.264. I can't figure out what to do in part (c) even though I know it's about conditional probability ...
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Statistical probability of coin landing on second flip
A coin is flipped twice in a row. The first result is heads. Is the statistical chance of the coin landing on heads on the second flip 50 percent or 25 percent?
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the expected norm of matrices with sub-gaussian entries
It is the exercise 4.4.6 in the book High-dimension-probability, https://www.math.uci.edu/~rvershyn/papers/HDP-book/HDP-book.pdf
Given the theorem that $$Prob\{||A||>CK(\sqrt m + \sqrt n +t)\} \leq ...
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Is this the correct way to get the $25^{th}$, $50^{th}$, and $75^{th}$ percentile?
From the frequency distribution in the image below,
$P_{25} = 0.25(53) = 13.25$
$13.25$ falls between index $1$ and $2$, so then $\dfrac{1+2}{2} = 1.5$, round up, $2$.
$P_{25} = 35.8\%$
$P_{50} = ...
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