Probability and Statistics Homework 4 PDF
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This document contains homework questions on probability and statistics, focusing on joint mass functions, marginal mass functions, covariance, correlation, and the independence of random variables. The problems involve finding marginal mass functions, specific probabilities, and evaluating the relationships between variables.
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Probability and Statistics Homework 4 November 2023 _____________________________________________________________________________ Due date: November 14, 2023 Upload in ADI a photo of your results, explaining all the steps. 1) Assume that (X,Y) has a joint mass function given by: 0 1 -1 0 0.25...
Probability and Statistics Homework 4 November 2023 _____________________________________________________________________________ Due date: November 14, 2023 Upload in ADI a photo of your results, explaining all the steps. 1) Assume that (X,Y) has a joint mass function given by: 0 1 -1 0 0.25 0 0.50 0 X Y 1 0 Find: a) The marginal mass functions b) 𝜇𝜇𝑋𝑋 , 𝜇𝜇𝑌𝑌 , 𝜎𝜎𝑋𝑋2 , and 𝜎𝜎𝑌𝑌2 c) 𝑃𝑃(𝑋𝑋 ≤ 0|𝑌𝑌 = 1) d) Cov(𝑋𝑋, 𝑌𝑌) e) ρ(𝑋𝑋, 𝑌𝑌) f) Are X and Y independent? g) Compare the results of e) and e). Explain. 0.25 2) Assume that (X,Y) has a joint mass function given by: 𝑓𝑓𝑋𝑋𝑋𝑋 (𝑥𝑥, 𝑦𝑦) = 𝑥𝑥+𝑦𝑦 𝑐𝑐 for x=1,2,3 and y=1,2,3 Find: a) Find the value of c such that c is a true joint mass function b) The marginal mass functions c) 𝜇𝜇𝑋𝑋 , 𝜇𝜇𝑌𝑌 , 𝜎𝜎𝑋𝑋2 , and 𝜎𝜎𝑌𝑌2 d) 𝑃𝑃(𝑌𝑌 ≤ 2|𝑋𝑋 = 3) e) Cov(𝑋𝑋, 𝑌𝑌) f) ρ(𝑋𝑋, 𝑌𝑌) g) Are X and Y independent?
