Students were requested to answer a question at schools and to state what is most important for them to succeed. Of many replies, one that that stood out was practice. Successful people surely are not born successful; they become successful through hard work and commitment. If you tend to get your goals, keep this in mind! followed below some question and answer examples that you can potentially benefit from to enhance your knowledge and gain insight that will assist you to continue your school studies.

## Question:

Which of the following is a valid probability distribution?

## Answer:

**Answer:**

The valid probability distribution is:

**Probability distribution D.**

**Step-by-step explanation:**

Probability distribution–

The probability distribution of a discrete variable is the list of the possible value ‘x’ and the probability of x at one trial.

The probability distribution for a variable x satisfies the following two properties:

- Each probability i.e. P(x) must lie between 0 and 1.

i.e. 0≤P(x)≤1.

- Sum of all the probabilities must be 1.

i.e. ∑ P(x)=1 .

Now we check which probability distribution satisfies this property:

**Probability Distribution A:**

x P(x)

1 0.2

2 0.2

3 0.2

4 0.2

5 0.2

6 0.2

—————————————

∑ P(x)=1.2≠1

**Hence, Probability distribution A is not a valid probability distribution.**

**Probability Distribution B:**

1 0.1

3 0.3

4 0.3

6 0.1

**Hence, Probability distribution B is not a valid probability distribution.**

**Probability Distribution C:**

3 0.4

4 0

5 0.1

∑ P(x)=0.9≠1

**Hence, Probability distribution C is not a valid probability distribution.**

**Probability Distribution D:**

2 0.1

3 0.1

4 0.5

5 0

∑ P(x)=1

Also,

for each x, 0≤P(x)≤1

**Hence, Probability distribution D is a valid probability distribution.**

They will be able to hopefully help the student take care of the question by working with the questions and answer examples. You can potentially then have a discussion with your classmate and continue the school learning by studying the subject jointly.