<h2>
Answer:</h2>
The valid probability distribution is:
Probability distribution D.
<h2>
Step-by-step explanation:</h2>
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:
<u>Probability Distribution A:</u>
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
<em>Hence, Probability distribution A is not a valid probability distribution.</em>
<u>Probability Distribution B:</u>
x P(x)
1 0.1
2 0.2
3 0.3
4 0.3
5 0.2
6 0.1
---------------------------------------
∑ P(x)=1.2≠1
<em>Hence, Probability distribution B is not a valid probability distribution.</em>
<u>Probability Distribution C:</u>
x P(x)
1 0.1
2 0.2
3 0.4
4 0
5 0.1
6 0.1
---------------------------------------
∑ P(x)=0.9≠1
<em>Hence, Probability distribution C is not a valid probability distribution.</em>
<u>Probability Distribution D:</u>
x P(x)
1 0.2
2 0.1
3 0.1
4 0.5
5 0
6 0.1
---------------------------------------
∑ P(x)=1
Also,
for each x, 0≤P(x)≤1
Hence, Probability distribution D is a valid probability distribution.
