In: Statistics and Probability

Determine whether the distribution is a discrete probability distribution. If not, state why.

x |
P(x) |

0 |
0.1 |

1 |
0.5 |

2 |
0.05 |

3 |
0.25 |

4 |
0.1 |

Given distribution is in table form.

x |
0 | 1 | 2 | 3 | 4 |

P(x) |
0.1 | 0.5 | 0.05 | 0.25 | 0.1 |

Check whether the distribution is a discrete probability distribution.

To be a discrete probability distribution, we must have a numerical random variable \(x\) such that \(P(x)\) must satisfy the preceding three requirements.

**1. **The variable \(x\) is a discrete random variable and its values are associated with probabilities.

**2.** \(\sum P(x)=P(0)+P(1)+P(2)+P(3)+P(4)\)

\(=0.1+0.5+0.05+0.25+0.1\)

\(=1\)

**3. **Each value of \(P(x)\) is between 0 and 1 .

The given table is a discrete probability distribution because it satisfies the discrete probability distribution's three requirements.

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