Question

State, with reasons, if the following probability distributions are admissible or not. $$ \begin{aligned} &\text { (i) }\\ &\begin{array}{|c|ccc|} \hline x: & 0 & 1 & 2 \\ \hline p(x): & 0-3 & 0 \cdot 2 & 0.5 \\ \hline \end{array} \end{aligned} $$ $$ \begin{aligned} &\text { (ii) }\\ &\begin{array}{|c|ccc|} \hline x: & -1 & 0 & 1 \\ \hline p(x): & 0 \cdot 4 & 0 \cdot 4 & 0 \cdot 3 \\ \hline \end{array} \end{aligned} $$ $$ \begin{aligned} &\text { (iii) }\\ &\begin{array}{|c|cccc|} \hline x: & 0 & 1 & 2 & 3 \\ \hline p(x): & 0 \cdot 2 & 0 \cdot 3 & 0 \cdot 3 & 0 \cdot 1 \\ \hline \end{array} \end{aligned} $$ $$ \begin{aligned} &\text { (iv) }\\ &\begin{array}{|r|ccccc|} \hline x: & -2 & -1 & 0 & 1 & 2 \\ \hline p(x): & 0 \cdot 3 & 0 \cdot 4 & -0 \cdot 2 & 0-2 & 0 \cdot 3 \\ \hline \end{array} \end{aligned} $$

Name: Problem 2, Chapter 13: BUSINESS STATISTICS
Uploaded: 2022-01-16T20:59:39-08:00
Duration: 2 min 26 s
Channel: Christopher Stanley
Description: State, with reasons, if the following probability distributions are admissible or not. (i) x: 0 1 2 p(x): 0-3 0 · 2 0.5 (ii) x: -1 0 1 p(x): 0 · 4 0 · 4 0 · 3 (iii) x: 0 1 2 3 p(x): 0 · 2 0 · 3 0 · 3 0 · 1 (iv) x: -2 -1 0 1 2 p(x): 0 · 3 0 · 4 -0 · 2 0-2 0 · 3

    State, with reasons, if the following probability distributions are admissible or not.
$$
\begin{aligned}
&\text { (i) }\\
&\begin{array}{|c|ccc|}
\hline x: & 0 & 1 & 2 \\
\hline p(x): & 0-3 & 0 \cdot 2 & 0.5 \\
\hline
\end{array}
\end{aligned}
$$
$$
\begin{aligned}
&\text { (ii) }\\
&\begin{array}{|c|ccc|}
\hline x: & -1 & 0 & 1 \\
\hline p(x): & 0 \cdot 4 & 0 \cdot 4 & 0 \cdot 3 \\
\hline
\end{array}
\end{aligned}
$$
$$
\begin{aligned}
&\text { (iii) }\\
&\begin{array}{|c|cccc|}
\hline x: & 0 & 1 & 2 & 3 \\
\hline p(x): & 0 \cdot 2 & 0 \cdot 3 & 0 \cdot 3 & 0 \cdot 1 \\
\hline
\end{array}
\end{aligned}
$$
$$
\begin{aligned}
&\text { (iv) }\\
&\begin{array}{|r|ccccc|}
\hline x: & -2 & -1 & 0 & 1 & 2 \\
\hline p(x): & 0 \cdot 3 & 0 \cdot 4 & -0 \cdot 2 & 0-2 & 0 \cdot 3 \\
\hline
\end{array}
\end{aligned}
$$

BUSINESS STATISTICS

S. C. Gupta and… 2nd Edition

Chapter 13, Problem 2

Instant Answer

Solved by Expert Christopher Stanley

01/16/2022

Step 1

Step 1: In order for a probability distribution to be admissible, the probabilities must satisfy the following conditions: Show more…

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State, with reasons, if the following probability distributions are admissible or not. $$ \begin{aligned} &\text { (i) }\\ &\begin{array}{|c|ccc|} \hline x: & 0 & 1 & 2 \\ \hline p(x): & 0-3 & 0 \cdot 2 & 0.5 \\ \hline \end{array} \end{aligned} $$ $$ \begin{aligned} &\text { (ii) }\\ &\begin{array}{|c|ccc|} \hline x: & -1 & 0 & 1 \\ \hline p(x): & 0 \cdot 4 & 0 \cdot 4 & 0 \cdot 3 \\ \hline \end{array} \end{aligned} $$ $$ \begin{aligned} &\text { (iii) }\\ &\begin{array}{|c|cccc|} \hline x: & 0 & 1 & 2 & 3 \\ \hline p(x): & 0 \cdot 2 & 0 \cdot 3 & 0 \cdot 3 & 0 \cdot 1 \\ \hline \end{array} \end{aligned} $$ $$ \begin{aligned} &\text { (iv) }\\ &\begin{array}{|r|ccccc|} \hline x: & -2 & -1 & 0 & 1 & 2 \\ \hline p(x): & 0 \cdot 3 & 0 \cdot 4 & -0 \cdot 2 & 0-2 & 0 \cdot 3 \\ \hline \end{array} \end{aligned} $$

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Key Concepts

Probability Mass Function (PMF)

A probability mass function is used to describe the distribution of a discrete random variable by assigning probabilities to each of its possible values. For a function to serve as a valid PMF, each assigned probability must lie within the interval [0, 1], and the entire set of probabilities must sum to exactly 1.

Non-negativity

One of the core properties of a valid probability distribution is non-negativity. This means that all individual probabilities associated with the outcomes must be zero or positive. Any negative probability value indicates an invalid distribution since probability cannot be less than zero.

Normalization Condition

The normalization condition requires that the sum of the probabilities for all possible outcomes equals 1. This condition ensures that the total probability across the entire sample space is properly accounted for, representing the certainty that some outcome will occur.

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