Probability and Statistics
Problems related to probability distributions, statistical inference, data analysis, etc.
Problems in this category
The problem asks to construct the cumulative distribution function (CDF), $F(x)$, for a discrete ran...
Cumulative Distribution FunctionCDFDiscrete Random VariableProbability DistributionStep Function
2025/4/8
A batch of products is produced by three different factories. The proportion of products from Factor...
ProbabilityLaw of Total ProbabilityConditional ProbabilityDefect Rate
2025/4/3
We are given that a batch of products is produced by three different factories. The proportion of pr...
ProbabilityConditional ProbabilityLaw of Total Probability
2025/4/3
A lens factory produces lenses. The probability of a lens breaking on the first drop is $\frac{1}{2}...
ProbabilityConditional ProbabilityIndependent Events
2025/4/2
A bag contains $r$ red balls and $t$ white balls. In each draw, a ball is randomly selected, its col...
ProbabilityConditional ProbabilityBalls and UrnsCombinatorics
2025/4/2
A lottery company creates lottery tickets with numbers from 00 to 99. The winning number is randomly...
ProbabilityLotteryMultiples
2025/4/2
The problem asks us to determine the potential genotypes of the parent plants given a partial Punnet...
GeneticsPunnett SquareProbabilityBiology
2025/4/2
The problem presents a partial Punnett square with two offspring genotypes, both $Rr$. We are asked ...
GeneticsPunnett SquareProbabilityAllelesGenotypes
2025/4/2
The problem describes a cross between two dragonflies where red body color is dominant over green bo...
GeneticsPunnett SquareAllelesProbability
2025/4/2
The problem requires drawing a frequency polygon based on the given rainfall data. The data is prese...
Frequency PolygonData VisualizationStatistics
2025/4/1