probability - How to generate multiple unrepeated random variables with a fixed non-uniform distribution? -

so given discrete distribution, (0.2, 0.4, 0.4), easy generate 1 random number follow distribution.

however, generate multiple unrepeated random numbers it?

e.g. distribution (p1 = 0.2, p2 = 0.4, p3 = 0.4), if generate

(1,2) p12 = 0.2,

(2,3) p23 = 0.6,

(1,3) p13 = 0.2.

i'm able have marginal distribution of

p1 = (p12 + p13)/2 = 0.2,

p2 = (p23 + p12)/2 = 0.4,

p3 = (p13 + p23)/2 = 0.4.

which same given distribution.

any idea build generator accomplish in terms of general distribution? thanks:)

if @ problem set of linear equations, able express using matrix equation. instance:

|1/2 1/2  0 |   |p12|     |p1| |1/2  0  1/2| * |p13|  =  |p2| | 0  1/2 1/2|   |p23|     |p3|

now can invert matrix get:

|p12|   | 1  1 -1|   |p1| |p13| = | 1 -1  1| * |p2| |p23|   |-1  1  1|   |p3|

in example produce:

|p12|   | 1  1 -1|   |0.2|   |0.2| |p13| = | 1 -1  1| * |0.4| = |0.2| |p23|   |-1  1  1|   |0.4|   |0.6|

so, p12 = p13 = 0.2 , p23 = 0.6.

Live one