Question

For what value of k the following distribution is a probability distribution?

X = xi:	0	1	2	3
P(X = xi):	2k4	3k2 - 5k3	2k - 3k2	3k-1

Answer 1

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