Probability and Statistics
Problems related to probability distributions, statistical inference, data analysis, etc.
Problems in this category
We are given three different hypothesis testing scenarios and we need to determine whether to reject...
Hypothesis Testingt-testsConfidence IntervalsStatistical SignificanceOne-tailed testTwo-tailed test
2025/4/23
We are asked to calculate the pooled variance from the given raw data for two groups. Group 1 has th...
VariancePooled VarianceSample VarianceStatistics
2025/4/22
We are given that out of 120 customers, 45 bought both bags and shoes. Also, everyone bought either ...
Venn DiagramsSet TheoryProbabilityInclusion-Exclusion Principle
2025/4/22
The problem asks us to find the probability that the absolute deviation of a normally distributed ra...
ProbabilityNormal DistributionStandard DeviationExpected ValueZ-scoreProbability Density Function
2025/4/22
The random variable $X$ is defined by its probability density function (PDF) $f(x)$ as follows: $f(x...
Probability Density FunctionCumulative Distribution FunctionIntegrationTrigonometry
2025/4/22
The problem provides a discrete random variable $X$ with its corresponding probabilities $P$. The pr...
Discrete Random VariableProbability Distribution FunctionExpected ValueVarianceStandard Deviation
2025/4/22
A person has 8 keys, only one of which opens a certain door. The person tries the keys at random, wi...
ProbabilityProbability DistributionDiscrete ProbabilityConditional Probability
2025/4/22
A fisherman has three favorite fishing spots. He visits each spot with equal probability. The probab...
ProbabilityLaw of Total ProbabilityConditional Probability
2025/4/22
A person has 8 keys, only one of which opens a door. They try the keys at random, excluding the used...
ProbabilityDiscrete Probability DistributionRandom VariableConditional ProbabilityPermutations
2025/4/22
A fisherman has three favorite fishing spots, which he visits with equal probability. The probabilit...
ProbabilityLaw of Total ProbabilityConditional Probability
2025/4/22