Question

Which of the following is a valid probability distribution?Probability Distribution AProbability Distribution BProbability Distribution CProbability Distribution D

Answer 1

If a distribution satisfies the following cases

Case 1

`0\leq p(x)\leq1`

Case 2

`\sum ^N_(n\mathop=1)p(x_n)=1`

Then the distribution is called a probability distribution.

In distribution A

`p(x)=0.2`

For each x but

`\sum ^{}_{}p(x)=0.2+0.2+0.2+0.2+0.2+0.2=1.2`

Hence it is not a probability distribution.

In B

`\sum ^{}_{}p(x)=0.1+0.2+0.3+0.3+0.2+0.1=1.2\\e1`

Hence this is not a probability distribution.

In the distribution C

`\sum ^{}_{}p(x)=0.1+0.2+0.4+0.1+0.1=0.9\\e1_{}`

Hence this is not a probability distribution.

In case of D

`\sum ^{}_{}p(x)=0.2+0.1+0.1+0.5+0+0.1=1`

And for all values of x

`0\leq p(x)\leq1`

Hence D is a valid probability distribution.