Probability and Statistics
Problems related to probability distributions, statistical inference, data analysis, etc.
Problems in this category
The problem describes a box plot showing the distribution of class sizes at Oceanside Middle School....
Box PlotData InterpretationQuartilesDescriptive Statistics
2025/5/16
A coffee shop chain wants to know if the average time customers spend in their stores during peak ho...
Hypothesis Testingt-testStatistical InferenceSample MeanSample Standard DeviationP-valueCritical Value
2025/5/15
The problem involves hypothesis testing for three different scenarios. Scenario 1: An e-commerce bus...
Hypothesis TestingZ-testT-testSample ProportionSample MeanP-valueSignificance LevelCritical Value
2025/5/15
Problem Statement 1: An e-commerce company wants to test if the proportion of satisfied customers is...
Hypothesis TestingZ-testT-testProportion TestMean TestStatistical Inference
2025/5/15
We are given three different problem scenarios that require hypothesis testing. For each scenario, w...
Hypothesis TestingZ-testT-testProportionsMeansP-valueCritical ValueStatistical Significance
2025/5/15
We are given that $\epsilon$ and $\lambda$ are uncorrelated random variables with variances $Var[\ep...
VarianceRandom VariablesLinear CombinationCovarianceUncorrelated Variables
2025/5/14
The problem asks for the probability that a random permutation of the letters in the word "PEPPER" y...
PermutationsProbabilityCombinatoricsWord Permutations
2025/5/14
We are given a discrete random variable $X$ that takes the values $-4, -2, -1, 2, 5, 6$ with equal p...
Discrete Random VariableVarianceExpected ValueProbability Distribution
2025/5/14
The problem states that the probability of an event occurring at least once in three independent tri...
ProbabilityIndependent EventsProbability of an Event Occurring at Least Once
2025/5/14
We are given three independent events A, B, and C with probabilities $P(A) = \frac{1}{2}$, $P(B) = \...
ProbabilityIndependent EventsSet TheoryProbability of UnionIrreducible Fractions
2025/5/14