Question

The following probability distribution graph has a missing value for the outcomes of x = 2 and x = 6. Note that x = {1, 2, 3, 4, 5, 6}.
Furthermore, P(x = 2) + 3P(x = 6) = 0.7
Determine the probability outcomes of both P(x = 2) and P(x = 6). Show all your work.
GRAPH:

0.4-

0.3- ---

0.2- ---
---
0.1-
1 2 3 4 5 6 2&6 are blank.

Answer 1

$$\begin{matrix} x & 1 & 2 & 3 & 4 & 5 & 6 \\ p(x) & 0.1 & a & 0.2 & 0.3 & 0.1 & b \end{matrix}$$

$$0.1+a+0.2+0.3+0.1+b=1$$ $$a+3b=0.7$$

$$a+b=0.3$$ $$a+3b=0.7$$

$$a+b=0.3$$ $$2b=0.4$$

$$a=0.1$$ $$b=0.2$$

$$\begin{matrix} x & 1 & 2 & 3 & 4 & 5 & 6 \\ p(x) & 0.1 & 0.1 & 0.2 & 0.3 & 0.1 & 0.2 \end{matrix}$$

$P(X=2)=0.1$

$P(X=6)=0.2$