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ProblemsClear skill: Joint Laws Build a practice set

ProblemCourse & topicStatus

PROB:9928201A sorting device independently sends each of six incoming pieces to tray A, B, or C, with probabilities 1/2, 1/3…

Joint LawsMultinomial DistributionMultinomial CoefficientsProbability 1 Problem Solving

Joint distributions and conditional expectationProbability I · Calculation

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PROB:9928202Six signals are classified independently as A, B, or C with probabilities 1/2, 1/3, and 1/6.

Joint LawsMarginal OF MultinomialBinomial DistributionProbability 1 Problem Solving

Joint distributions and conditional expectationProbability I · Calculation

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PROB:9928203Each of eight independent service requests receives exactly one label: A, B, C, or D, with probabilities 1/10,2/10,…

Joint LawsAggregation OF CategoriesMultinomial DistributionBinomial DistributionProbability 1 Problem Solving

Joint distributions and conditional expectationProbability I · Calculation

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PROB:9928204Six independent packets have types A, B, or C with probabilities 1/2,1/3,1/6.

Joint LawsConditioning ON A CountConditional MultinomialMarginal OF MultinomialProbability 1 Problem Solving

Joint distributions and conditional expectationProbability I · Calculation

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PROB:9928205Ten independent observations fall into categories A, B, or C with probabilities 1/5,3/10,1/2.

Joint LawsIndicator MethodMultinomial CovarianceVariance OF A SumProbability 1 Problem Solving

Joint distributions and conditional expectationProbability I · Calculation

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PROB:9928206Seven objects are independently classified as A, B, C, or D with probabilities 1/10,2/10,3/10,4/10.

Joint LawsConditional MultinomialConditioning ON A CountAggregation OF CategoriesProbability 1 Problem Solving

Joint distributions and conditional expectationProbability I · Calculation

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PROB:9928207Twelve independent requests are classified as urgent, routine, or deferred, with probabilities 1/5, 3/10, and 1/2,…

Joint LawsMultinomial DistributionWeighted TotalsIndicator MethodProbability 1 Problem Solving

Joint distributions and conditional expectationProbability I · Calculation

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PROB:9928208Nine independent arrivals choose desks A,B,C with probabilities 1/6,1/3,1/2.

Joint LawsMultinomial DistributionConditioning ON A CountBinomial SplittingProbability 1 Problem Solving

Joint distributions and conditional expectationProbability I · Calculation

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PROB:9928209Eight independent readings fall into four categories with probabilities (1/10,1/5,3/10,2/5).

Joint LawsMultinomial DistributionCategory GroupingMultinomial TheoremProbability 1 Problem Solving

Joint distributions and conditional expectationProbability I · Calculation

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PROB:9928210Five independent signals are classified as A,B,C, with probabilities 1/2,1/4,1/4.

Joint LawsMultinomial DistributionDisjoint CasesConditional ProbabilityProbability 1 Problem Solving

Joint distributions and conditional expectationProbability I · Calculation

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PROB:9928211Three independent parcels are assigned to lockers A,B,C, with probabilities 1/2,1/4,1/4.

Joint LawsIndicator MethodOccupancy CountsCovariance OF IndicatorsProbability 1 Problem Solving

Joint distributions and conditional expectationProbability I · Calculation

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PROB:9928212Mathematical problem title

Joint LawsFinite Joint DistributionsConditional DistributionConditional ExpectationProbability 1 Problem Solving

Joint distributions and conditional expectationProbability I · Calculation

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PROB:9928213A bag contains three red, two blue, and two green counters, all distinct.

Joint LawsMultivariate HypergeometricConditional DistributionSampling Without ReplacementProbability 1 Problem Solving

Joint distributions and conditional expectationProbability I · Calculation

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PROB:9928214Two independent trials each produce one of the labels A, B, C.

Joint LawsNonidentical TrialsIndicator MethodMultinomial CovarianceProbability 1 Problem Solving

Joint distributions and conditional expectationProbability I · Calculation

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PROB:9928215Choose a coin once: with probability 1/2 choose a coin whose heads probability is 1/4, and otherwise choose one…

Joint LawsMixture DistributionsConditional IndependencePredictive ProbabilityProbability 1 Problem Solving

Joint distributions and conditional expectationProbability I · Calculation

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PROB:9928216Mathematical problem title

Joint LawsPairwise IndependenceMutual IndependenceFinite Joint DistributionsProbability 1 Problem Solving

Joint distributions and conditional expectationProbability I · Calculation

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PROB:9928217The variable X takes the values -2,-1,0,1,2 with respective probabilities 1/8,1/4,1/4,1/4,1/8.

Joint LawsZero CovarianceConditional ExpectationDeterministic TransformationsProbability 1 Problem Solving

Joint distributions and conditional expectationProbability I · Calculation

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PROB:9928218Choose N=1 or N=3, each with probability 1/2.

Joint LawsTotal VarianceRandom Sample SizeConditional CovarianceProbability 1 Problem Solving

Joint distributions and conditional expectationProbability I · Calculation

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PROB:9928219A random point (X,Y) has constant joint density c on the triangle 0<x<y<2, and density zero elsewhere.

Joint LawsTriangular SupportMarginal DensitiesConditional DensitiesProbability 1 Problem Solving

Joint distributions and conditional expectationProbability I · Calculation

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PROB:9928220The joint density of (X,Y) is c(x+2y) on 0<x<1,\ 0<y<1, and zero elsewhere.

Joint LawsDensity NormalizationConditional DensitiesIntegration RegionsProbability 1 Problem Solving

Joint distributions and conditional expectationProbability I · Calculation

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PROB:9928221Choose three independent points uniformly from the interval (0,2).

Joint LawsOrder StatisticsRange DistributionJoint DensitiesProbability 1 Problem Solving

Joint distributions and conditional expectationProbability I · Calculation

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PROB:9928222Mathematical problem title

Joint LawsChange OF VariablesJacobianDensity FactorizationProbability 1 Problem Solving

Joint distributions and conditional expectationProbability I · Calculation

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PROB:9928223Let N have a Poisson distribution with mean three.

Joint LawsPoisson SplittingJoint Mass FactorizationConditional MultinomialProbability 1 Problem Solving

Joint distributions and conditional expectationProbability I · Calculation

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PROB:9928224Mathematical problem title

Joint LawsDiscrete TransformationsParity ConstraintsConditional DistributionProbability 1 Problem Solving

Joint distributions and conditional expectationProbability I · Calculation

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Showing 24 of 64 matching problems.

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The pair (X,Y) takes values in

\{0,1,2\}^2

.

Let U,V be independent and uniform on

\{0,1,2\}

.

The pair

(X,Y)

has joint density

f_{X,Y}(x,y)=xy e^{-(x+y)},\qquad x>0,\ y>0

, and density zero elsewhere.

Let X be uniform on

\{0,1,2,3\}

and Y uniform on

\{0,1,2\}

, independently.