Which of the following are valid probability distributions for a discrete random variable

Mathematics

2 answers:

Radda [10]3 years ago

8 0

All of them except B and C. Probabilities must add to 1 and none of the p's can be negative

Kipish [7]3 years ago

8 0

The valid probability distributions for a discrete random variable are :

<h2>Option A , D , and E</h2>

<h3>Further explanation</h3>

The probability of an event is defined as the possibility of an event occurring against sample space.

Let us tackle the problem.

In a discrete random variable , the sum of all the probability of distributions must equal to 1. The minimum value of probability is 0 and the maximum value of probability is 1.

<h2>Option A :</h2>

$\frac{1}{6} + \frac{1}{6} + \frac{1}{6} + \frac{1}{6} + \frac{1}{6} + \frac{1}{6} = \frac{6}{6} = 1$ ✔

This is the valid probability distributions for a discrete random variable

<h2>Option B :</h2>

$\frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6} = \frac{19}{20} \ne 1$ ⤬

This is not the valid probability distributions for a discrete random variable

<h2>Option C :</h2>

$-\frac{1}{2} - \frac{1}{3} - \frac{1}{4} - \frac{1}{5} + \frac{137}{60} = 1$ ⤬

Although the sum is 1 but this is still not the valid probability distributions for a discrete random variable because probability cannot have negative values.

<h2>Option D :</h2>

$\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + ... + \frac{1}{128} = 1$ ✔