Nov 3, 2006 #1 T tomshack Junior Member level 3 Joined Mar 4, 2006 Messages 27 Helped 0 Reputation 0 Reaction score 0 Trophy points 1,286 Activity points 1,474 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 )
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 )
Nov 4, 2006 #2 D dazhen Member level 3 Joined Nov 23, 2004 Messages 56 Helped 2 Reputation 4 Reaction score 0 Trophy points 1,286 Location In the Mountain Activity points 437 tomshack said: 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 ) Click to expand... 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.
tomshack said: 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 ) Click to expand... 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.