Question

fill in the \\(p(x=x)\\) values to give a legitimate probability distribution for the discrete random variable \\(x\\), whose possible values are 0, 2, 4, 5, and 6.

\\(\

$$\begin{array}{|c|c|} \\hline \\text{value } x \\text{ of } x & p(x=x) \\\\ \\hline 0 & 0.13 \\\\ \\hline 2 & 0.28 \\\\ \\hline 4 & \\square \\\\ \\hline 5 & \\square \\\\ \\hline 6 & 0.16 \\\\ \\hline \\end{array}$$

\\)

Explanation:

State the requirements for a legitimate probability distribution

Using the Probability Distribution and Discrete Random Variable knowledge points

$$
LATEXBLOCK0
$$

Calculate the sum of the known probabilities

Using the Probability Distribution knowledge point

$$
LATEXBLOCK1
$$

Determine the remaining probability to distribute

Using the Probability Distribution knowledge point

$$
LATEXBLOCK2
$$

Choose valid values for the missing probabilities

Using the Probability Distribution knowledge point

$$
LATEXBLOCK3
$$

Answer:

Fill in the \(P(X=x)\) values to give a legitimate probability distribution for the discrete random variable \(X\), whose possible values are 0, 2, 4, 5, and 6.

Value \(x\) of \(X\)	\(P(X=x)\)
2	0.28
4	<blank>0.20</blank>
5	<blank>0.23</blank>
6	0.16

(Note: Any two non-negative values that sum to 0.43 are mathematically correct.)