please help about this problem ,or hint

[tomshack]

For some integer L and contant c,two discrete random variable have a joint probility mass function given by

P( m,n) = c m ≥ 0,n ≥ 0 , m+n < L
0 otherwise

A) find the value of the constant c in terms of L
b) find the marginal PMFs ,P(m) and P
c) find P(M+N<L/2 )

 

[dazhen]

For some integer L and contant c,two discrete random variable have a joint probility mass function given by

P( m,n) = c m ≥ 0,n ≥ 0 , m+n < L
0 otherwise

A) find the value of the constant c in terms of L
b) find the marginal PMFs ,P(m) and P
c) find P(M+N<L/2 )

A) ∫∫P(m,n)•dm•dn=1 --> c*½*L²=1 --> c=2/L²,

B) P(m)=∫P(m,n)dn from -∞ to ∞
categorize m to three range (-∞,0), (0, L), (L, ∞),

follow the similar way, to find P;

C) P(m+n<L/2)=∫∫c•dm•dn =½(L/2)²•c=¼.

draw a picture like this will help you sort things out.