Question

is the following table correct?

x	p(x)	x*p(x)
1	0.10	0.10
2	0.05	0.10
3	0.10	0.30
4	0.15	0.60
5	0.30	1.50
6	0.20	1.20
7	0.10	0.7

a. yes
b. no

Explanation:

Step1: Check sum of probabilities

The sum of all $P(x)$ values in a probability - distribution should be 1. Calculate $\sum_{i = 1}^{7}P(x_i)=0.10 + 0.05+0.10 + 0.15+0.30+0.20+0.10=1$.

Step2: Check calculation of $x\cdot P(x)$

For $x = 1$, $1\times0.10 = 0.10$; for $x = 2$, $2\times0.05=0.10$; for $x = 3$, $3\times0.10 = 0.30$; for $x = 4$, $4\times0.15=0.60$; for $x = 5$, $5\times0.30 = 1.50$; for $x = 6$, $6\times0.20=1.20$; for $x = 7$, $7\times0.10 = 0.70$. All calculations of $x\cdot P(x)$ are correct.

Answer:

a. Yes