Question

2. f(x,y) = (xy a joint probability density function over the range 0 SX S4 and 0 Sy sx. Then, determine the following: a) P(x < 1,Y <2) b) P(1<x<2) c) P(Y>1)

Answer 1

Sol Given Given that f(x,y) = 6 ay which is a joint porobability density tu OS Xcy and OsYcx. (a) To determine P(x<1,722) :- over the gange int probability density function p(xci, v<2) = 5 5 ss nyay do 2 se s'ents conta de ** [[3-6]á 52 / 2(220)dx I a.2 dx (2) ('die de

P(xer,y<x) - ] P(x1,y<x) = b) 1o detesmine ?[1<x<2) :-

f2 = 1**.ydy flans to be a Sydy 32 flag = 10 11 ] f(u) = ( ) flag = 2 l jost=4 Noo (1<<< 2) = 2 x de jocx <4

36 = (ex-1/ (54) = 1- 157 [0- :: : (+) 2 - s a ht ** % = {6 217)

(c) To determine plys) (0) - "зи 3-4. "fiy = 5 ... 2 الں - Г (s) o" ]> - «~] fly) = use xy f(3) = 2

Now Ply>u) = 1-P (Y<1) Ply=1= 1- S (*) dy Ply>u) = 1 =1-1*-] [P(y>) = 32 clothed