Homework 4.pdf

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?