# Which of the following is a valid probability distribution?

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## Question:

Which of the following is a valid probability distribution?

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.

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