Question
Question: Random variable X has its range = {0, 1, 2} and their probabilities are given by P(x=0) = 3k<sup>3</...
Random variable X has its range = {0, 1, 2} and their probabilities are given by P(x=0) = 3k3, P(x=1) = 4k – 10k2. P(x=2) = 5k-1. Then k =
(i) Mean (ii) SD
A
1/3
B
8/9
C
14/9
D
1
Answer
1/3
Explanation
Solution
(i) 3k3 – 10k2 + 9k – 1 = 1
3k3 – 10k2 + 9k – 2 =0
(k – 1)(k – 2)(3k – 1) = 0
k = 1,2, 1/3
For k = 1,2, P(x=0) is more than 1
⇒ k = 1/3