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Joint Discrete Distributions worksheets

Use numeric joint PMF tables for CDFs, events, marginals, conditionals, moments, and independence.

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Every task prints the table, density support, paired observations, histogram bins, or sampling assumptions needed to reproduce the result.

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Calculate from a complete finite joint PMF.

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Verify support and total probability.

Support and normalization determine valid sums or integrals.

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  • Label support and units.
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Math SheetNameScoreTeacherDateJoint Discrete DistributionsUse the complete labeled joint PMF table. Show normalization, requested sums, and marginal products before deciding independence.1.3x3 table. Rows X=68,69,70; columns Y=166,167,168; weights / 36: 1,2,3 / 2,4,6 / 3,6,9. Find the full conditional PMF of Y given X=70.Assumptions: The displayed support is complete; omitted pairs have probability 0.Independence requires equality in every cell.2.2x3 table. Rows X=82,83; columns Y=194,195,196; weights / 18: 1,2,3 / 2,4,6. Find F(82,195).Assumptions: The displayed support is complete; omitted pairs have probability 0.Independence requires equality in every cell.Show support, sums or integrals, and approximation assumptions.math-sheet.comPage 1 of 4
Math SheetNameScoreTeacherDateJoint Discrete DistributionsUse the complete labeled joint PMF table. Show normalization, requested sums, and marginal products before deciding independence.3.2x3 table. Rows X=7,8; columns Y=44,45,46; weights / 45: 6,11,5 / 10,4,9. Find E(X), E(Y), E(XY).Assumptions: The displayed support is complete; omitted pairs have probability 0.Independence requires equality in every cell.4.2x2 table. Rows X=12,13; columns Y=54,55; weights / 9: 1,2 / 2,4. Find P(X=13 or Y=54).Assumptions: The displayed support is complete; omitted pairs have probability 0.Independence requires equality in every cell.Show support, sums or integrals, and approximation assumptions.math-sheet.comPage 2 of 4
Math SheetNameScoreTeacherDateJoint Discrete DistributionsUse the complete labeled joint PMF table. Show normalization, requested sums, and marginal products before deciding independence.5.2x3 table. Rows X=4,5; columns Y=38,39,40; weights / 18: 1,2,3 / 2,4,6. Are X and Y independent? Check every cell.Assumptions: The displayed support is complete; omitted pairs have probability 0.Independence requires equality in every cell.6.2x3 table. Rows X=-65,-64; columns Y=-100,-99,-98; weights / 26: 0,4,9 / 3,8,2. Find both full marginal PMFs.Assumptions: The displayed support is complete; omitted pairs have probability 0.Independence requires equality in every cell.Show support, sums or integrals, and approximation assumptions.math-sheet.comPage 3 of 4
Math SheetNameScoreTeacherDateJoint Discrete DistributionsUse the complete labeled joint PMF table. Show normalization, requested sums, and marginal products before deciding independence.7.3x3 table. Rows X=-52,-51,-50; columns Y=-74,-73,-72; weights / 36: 1,2,3 / 2,4,6 / 3,6,9. Find c and identify zero-probability cells.Assumptions: The displayed support is complete; omitted pairs have probability 0.Independence requires equality in every cell.8.2x3 table. Rows X=43,44; columns Y=116,117,118; weights / 33: 4,9,3 / 8,2,7. Find both full marginal PMFs.Assumptions: The displayed support is complete; omitted pairs have probability 0.Independence requires equality in every cell.Show support, sums or integrals, and approximation assumptions.math-sheet.comPage 4 of 4

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