b) Find 𝑝𝑌 (𝑦), the marginal p.m.f. of 𝑌

ind 𝑝𝑌 (𝑦), the marginal p.m.f. of 𝑌

eet the joint p.d.f. of X1 and X2 be:ℎ(𝑥1, 𝑥2) = {8𝑥1𝑥2 for 0 < 𝑥1 < 𝑥2 < 10 otherwisea) Find the joint p.d.f. of 𝑌1 = 𝑋1𝑋2and 𝑌2 = 𝑋2b) Are 𝑌1 and 𝑌2 independent? Why? (10 points

G) For two random variables 𝑋 and 𝑌, 𝐸(𝑋𝑌) = 𝐸(𝑋)𝐸(𝑌) hold if 𝑋 and 𝑌 are _______

For the Joint PMF as shown, find each of following quantities:𝑝𝑋 𝑥 , 𝑝𝑌 𝑦 , 𝑝𝑋|𝑌 𝑥 𝑦 , 𝑝𝑌|𝑋 𝑦 𝑥 , 𝐸[𝑋|𝑌 = 3]Also find whether 𝑋 and 𝑌 are independent or not.[The graph shows 𝑝𝑋,𝑌(𝑥, 𝑦)/12]

Let (𝑋, 𝑌 ) be a discrete bivariate random vector with joint p.m.f. given by𝑓𝑋,𝑌 (𝑥, 𝑦) =(𝑐 · 𝑥𝑦 if 𝑥 ∈ {1, 2, 3}, 𝑦 ∈ {1, 2, 3}0 otherwisewhere 𝑐 > 0 is an as-of-yet undetermined constant.(a) Find the value of 𝑐