Question

Suppose that the following table is the joint probability distribution of two random variables X and Y: х -2 0 2 3 0.27 0.08 0.16 0.2 0.1 0.04 0.1 0.05 a. Find the marginal PDF of X when x=-2, 0, 2, and 3. b. Find the marginal PDF of Y when y=2 and 5. . Find the conditional PDF of x=-2 and 3 given that y=2 has occurred. . Find the conditional PDF of y=2 and 5 given that x=3 has occurred. 2. State conditional PDF in terms of Joint and marginal PDFs.

Answer 1

Soluzioni Ч \Х І pe -2 0 2 3 10.27 0.08 0.16 0.2 0.04 0.110.05 rutul 10.37 10.12 10. 260.25 Totu) 0.71 0. 29 1.00 marginal p.dor of "x is X IPTX2002 -210 | 23 Tota) 0.37 0.12 0.26 0-25 1.00 16 marginal pidl:f ufy is l y Il peyzji 2 0.71 L s 0.29 total.. 100 o condirundlp. d. f of X2-2 given.y:2 9, (X20/4=2) T Total X 1-2 TOT 2 lg(xly2) | 0.22 0.08 0.16 0-71 0.71 10.71 3 0. 2 0.7) 00

Date conditional podof of xa-244 3 given y = 2 X - (x2/22) 21 J513:31422) 2 20 conditional podoful 12-3 4 S 2 ___0.2 hral ७.05 0.25 0.25 25 & conditional poder uf y 22 45 given X=3 १. (५ :-/x23) = 20 १. (५:5/x23) : Tra conditional podofur x giren y is )- 31001 example : 9(X : -2 /12 2 ) : f (w.y) , (५) 21130

0.27 0.71 g, fx/y=2) 27 71 pdof of ylx is f condiñonal dinero 9₂ (Y/82x) = f(x,y) fica] example 9. 19=2}x=3) f(X²3,922) f11823) 0.2 0.25 2S 92/422/X23).