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 the sum of probabilities

The sum of all probabilities \(P(x)\) in a probability distribution must be \(1\).

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

For \(x = 2\), \(x\cdot P(x)=2\times0.05 = 0.10\)
For \(x = 3\), \(x\cdot P(x)=3\times0.10=0.30\)
For \(x = 4\), \(x\cdot P(x)=4\times0.15 = 0.60\)
For \(x = 5\), \(x\cdot P(x)=5\times0.30=1.50\)
For \(x = 6\), \(x\cdot P(x)=6\times0.20 = 1.20\)
For \(x = 7\), \(x\cdot P(x)=7\times0.10=0.70\) (not \(0.7\), but in terms of the nature of the problem, if we consider significant - figure or decimal - place tolerance, and since the main check is on the probability sum (which is correct) and the general structure of the table (assuming the \(x\cdot P(x)\) values are just written with a possible minor decimal - place notation issue rather than a calculation error).

Answer:

A. Yes