Problems on joint probability density function
1. The joint p.d.f of the random variable (X,Y) is given
𝑥2
𝑥𝑦 2 + ; 0 < 𝑥 < 2, 0 < 𝑦 < 1
by 𝑓ሺ 𝑥, 𝑦 ሻ = ቊ 8
0; 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
(i) Marginal density function of X and Y
1
(ii) 𝑃[𝑋 > 1/ 𝑌 < 2 ]
(iii) 𝑃[𝑋 > 1]
1
(iv) 𝑃[𝑌 < ]
2
(v) 𝑃[𝑋 < 𝑌]
(vi) 𝑃[𝑋 + 𝑌 ≤ 1]
, The region of integration
1. The joint p.d.f of the random variable (X,Y) is given
𝑥2
𝑥𝑦 2 + ; 0 < 𝑥 < 2, 0 < 𝑦 < 1
by 𝑓ሺ 𝑥, 𝑦 ሻ = ቊ 8
0; 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
(i) Marginal density function of X and Y
1
(ii) 𝑃[𝑋 > 1/ 𝑌 < 2 ]
(iii) 𝑃[𝑋 > 1]
1
(iv) 𝑃[𝑌 < ]
2
(v) 𝑃[𝑋 < 𝑌]
(vi) 𝑃[𝑋 + 𝑌 ≤ 1]
, The region of integration
