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