For what value of k the following distribution is a probability distribution?
The probability distribution of X is:
We Know that
Therefore,
2k4+3k2-5k3+2k-3k2+3k-1=1
2k4-5k3+5k-2=0
2(k4-1)-5k2-1)=0
2(k2-1)(k2+1)-5k(k-1)(k+1)=0
2(k-1)(k+1)(k2+1)-5k(k-1)(k+1)=0
(k-1)(k+1)(2(k2+1)-5k=0
(k-1)(k+1)(2k2-5k+2)=0
(k-1)(k+1)(2k2-k-4k+2)=0
(k-1)(k+1)(k(2k-1)-2(2k-1))=0
(k-1)(K+1)(2k-1)(k-2)
k-1=0
K+1=0
2k-1=0
k-2=0