The probability distribution function of a discrete variable X is given by: P(X=r) = kr, r=1,2,3,...,n, where k is a constant. Show that #k=2/(n(n+1))# ?
#k=2/(n(n+1))#
1 Answer
See the proof below.
Explanation:
The sum of the probabilities must be equal to
#sumP(X=r)=sum_(r=1)^nkr=1#
Therefore,
#ksum_(r=1)^nr=1#
We know that the sum of the first
#sum_(r=1)^n r=n/2(n+1)#
So,
#k*n/2(n+1)=1#
#k=2/(n(n+1))#
