Answer:
[tex]c = \dfrac{1}{21}[/tex]
[tex]\text{P(X is odd)} = \dfrac{3}{7}[/tex]
Step-by-step explanation:
We are given the following in the question:
X: {1, 2, 3, 4, 5, 6}
[tex]p(k) = ck[/tex]
where c is a constant.
a) Value of c
The summation of all the probabilities for a discrete distribution should be 1.
[tex]\displaystyle\sum P(X=x) = 1\\\\P(1) +P(2) +P(3) +P(4) +P(5) +P(6) = 1\\c + 2c + 3c + 4c + 5c + 6c = 1\\21c = 1\\c = \dfrac{1}{21}[/tex]
[tex]p(k) = \dfrac{k}{21}[/tex]
b) P(X is odd)
[tex]=P(1) + P(3) + P(5)\\\\=\dfrac{1}{21} + \dfrac{3}{21} + \dfrac{5}{21}\\\\=\dfrac{9}{21} = \dfrac{3}{7}[/tex]
