Question

Question !
If X and Y are two independent Poisson random variables with parameters 2
and 1 respectively then distribution of X+Y is ...​

Answer 1

Step-by-step explanation:

For

X=0 and Y=3,

we get

P=

5

C

0

2

1

5

.

7

C

3

2

1

7

=

4096

35

...(i)

For

X=1 and Y=2,

we get

P=

5

C

1

2

1

5

.

7

C

2

2

1

7

=

4096

105

...(ii)

For

X=2 and Y=1,

we get

P=

5

C

2

2

1

5

.

7

C

1

2

1

7

=

4096

70

...(iii)

For

X=3 and Y=0,

we get

P=

5

C

3

2

1

5

.

7

C

0

2

1

7

=

4096

10

...(iv)

Adding i ii, iii and iv.

we get

4096

35+105+70+10

=

4096

220

=

1024

55