Questions tagged [statistics]
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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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Conditional expectation on squared sum of independent random variables
Given $X$ and $Y$ independent random variables of means $0$ and variance equal to $\sigma^2$, and $Z = X + Y$, find the conditional expectation $E[Z^2|X = x]$ for any value $x$ where the conditional ... probability statistics statistical-inference conditional-expectation- 82
Can I derive the first moment when I am know the second and forth?
So I know what $E[X^2]$ and $E[X^4]$ are and I need the first moment. Would it be a right approach for me to use the equality below $$E[X^4] - E[X^2] = (E[X^2] - E[X^1])\times(E[X^2] - E[X^1])$$ If ... statistics maximum-likelihood- 45
If set $C$ has 60 elements, and set $B_i$ has 9 elements randomly sampled from $C$, what is the mean value of $i$ to seeing all elements of $C$?
This question is inspired by the Yu-Gi-Oh TCG. Every so often, the game receives a new set containing either 60 or 100 new cards (this is the set $C$ in the question title). However, they don't just ... probability statistics- 333
Given the input and output for a function, I need to find the optimal coefficients.
Consider this function: Polynomial Function With k1 ... k5 being the coefficients and k6 being another constant. The coefficients and the constants do not have any constraints. What would be a good ... statistics machine-learning regression regression-analysis- 1
Union over two sets within which a pattern is statistically significant
If I have two variables $f_{a}$ and $f_{b}$ (let's say they are sampled from a Poisson point process and are thus independent) which form a pattern $C$ via some association rule. Now if this pattern ... probability statistics probability-distributions hypothesis-testing point-processes- 21
What can we conclude given that A is independent of B but not C?
Suppose A and C are dependent random variables. If B is independent of A, can one conclude that B is also independent of C? probability statistics independence- 1,297
Normalize comparison of results based on two metrics: average result score and total volume of results [closed]
I have an analysis where I am attempting to rank store locations based on customer reviews. Each review a store receives will have a score between 1-10 and there is a variable number of reviews per ... statistics- 103
Equivalence between Bayes Threshold and Neyman Pearson Threshold?
I could not find an answer to this question, so it's probably obvious to everyone else: This question concerns binary hypothesis testing ($\mathcal{H}_{0}$ versus $\mathcal{H}_{1}$) against data $\... probability statistics probability-distributions hypothesis-testing- 309
What is probability that an arbitrarily selected person is either female or has chosen $B$
Given is Female total 2500, male total 2000 =total 4500 Party B: female 150, male 700 What is probability that an arbitrarily selected person is either female or has chosen B! I thought of doing 2500+... probability statistics- 11
Branching Process and the offspring distribution
Explain why {Xn, n ≥ 0} is a branching process with X0 = 1 and the offspring distribution: f0 = 1/12, f1 = 2/3, f2 = 1/4. Calculate the probability of the event that there are no red cells at time 2.5.... probability statistics stochastic-processes poisson-distribution- 1
Order Statistics & First Order Stochastic Dominance
Does the distribution of a the second order statistic of a distribution dominate (i.e., FOSD) the distribution of the first order statistic? I assume that it does, but it would be very helpful if a ... statistics probability-distributions order-statistics- 141
Paradox of Probability Distribution Functions
(Adjusted for comments) This is a problem I have tried to work out for a while: We can not take the integral of a probability density function at a single point - as a matter of fact, we can not take ... probability integration statistics normal-distribution- 1,832
SSN randomization: how many numbers are available?
The Social Security Administration Number Randomization Frequently Asked Questions states that The nine-digit SSN will eventually be exhausted. The previous SSN assignment process limited the number ... statistics- 103
Probability regarding yellow and white cabs and two independent witnesses
20% of the cabs are white and the other 80% are yellow. A cab was involved in an accident and ran away. An eyewitness to the accident claims that the cab was yellow. Knowing that eyewitness tell the ... probability statistics permutations combinations- 29
Probability regarding 3 random toppings on a pizza
At Luigi’s House of Random Pizza, you can order only one thing: A medium pizza with three random topping layers chosen by Luigi himself. Luigi has the following toppings: Pepperoni, Pineapple, ... probability combinatorics statistics- 29
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