Question

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

Answer 1

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

Answer 2

The valid probability distributions for a discrete random variable are :

Option A , D , and E

Further explanation

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.

Option A :

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

This is the valid probability distributions for a discrete random variable

Option B :

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

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

Option C :

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

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.

Option D :

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

This is the valid probability distributions for a discrete random variable

Option E :

$\frac{1}{5} + \frac{1}{10} + \frac{1}{10} +...+ \frac{1}{10} = 1$ ✔

This is the valid probability distributions for a discrete random variable

Learn more

• Different Birthdays : brainly.com/question/7567074
• Dependent or Independent Events : brainly.com/question/12029535
• Mutually exclusive : brainly.com/question/3464581

Answer details

Grade: High School

Subject: Mathematics

Chapter: Probability

Keywords: Probability , Sample , Space , Six , Dice , Die