Which of the following is a valid probability distribution?

The valid probability distribution is:

Probability distribution D.

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:

                         i.e. 0≤P(x)≤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:

        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

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

Probability Distribution C:

        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

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

Probability Distribution D:

        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.

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step-by-step explanation:

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3     x =27

8)17.80