throw two six-sided dice, one is fair and the other is unfair with probabilities given as Face : 1 2 3 4 5 6 Pobability : 1/9 1/9 1/9 1/9 3/9 2/9 The unfair die look the same as the fair die. Let X and Y be the number observed from the fair unfair dice, respectively. A)Find the joint distribution of X and Y

Probability is that the branch of arithmetic regarding numerical descriptions of however possible an occasion is to occur, or however possible it's that a proposition is true.

Main body:

Two dice are thrown S = { (i,j) / i, j =1:6}

a) X : Number observed from the fair die.

Y : Number observed from the unfair die.

P(X=1, Y=1) = 1/6 * 1/9 =1/54

Similarly we can obtained remaining probabilities.

P(X=2, Y=2 ) = 1/6 * 1/9 =1/54

P(X=3, Y=3 ) = 1/6 * 1/9 =1/54

P(X=4, Y=4 ) = 1/6 * 1/9 =1/54

P(X=5, Y=5 ) = 1/6 * 3/9 =3/54 = 1/18

P(X=6, Y=6 ) = 1/6 * 2/9 =2/54 = 1/27

the joint distribution of X and Y is =

⇒P(X=1, Y=1) = 1/6 * 1/9 =1/54 + P(X=2, Y=2 )+ P(X=3, Y=3 ) + P(X=4, Y=4)+

P(X=5, Y=5 ) +P(X=6, Y=6 )

⇒1/54 +1/54+1/54+1/54 +3/54+2/54

⇒ 9/54

⇒1/6

Hence the joint distribution of X and Y probability is 1/6.

To know more about probability , visit:

https://brainly.com/question/24756209

#SPJ4