Question

Determine whether the distributions below are probability distributions. If not, what characteristic of the distribution is the reason? Bulleye Hit Darts X P(X = x) 0 0.64 1 0.26 2 0.18 3 0.04 4 -0.12

Bullseye's Hit in Darts X P(X = x) 0 0.69 1 0.16 2 0.12 3 0.08 4 0.03

Bullseye's Hit in Darts X P(X = x) 0 0.57 1 0.26 2 0.11 3 0.04 4 0.02

Bullseye's Hit in Darts X P(X = x) 0 0.53 1 0.24 2 0.11 3 0.04 4 0.02

Answer 1

From the given information,

We know that,

The conditions required to be probability distribution are,

i. All probabilities should be greater than or equal to zero.

ii. Sum of all probabilities should be equal to 1.

Consider,

a. Bulleye Hit Darts X P(X = x) 0 0.64 1 0.26 2 0.18 3 0.04 4 -0.12

Here, P(X=4)=-0.12<0

Hence, This is not probability distribution.

b. Bullseye's Hit in Darts X P(X = x) 0 0.69 1 0.16 2 0.12 3 0.08 4 0.03

Here, Sum of all probabilities is 1.08 which is not equal to 1.

Hence, This is not probability distribution.

c. Bullseye's Hit in Darts X P(X = x) 0 0.57 1 0.26 2 0.11 3 0.04 4 0.02

Here, All probabilities are greater than or equal to zero and also sum of all probabilities is 1.

Hence, This is probability distribution.

d. Bullseye's Hit in Darts X P(X = x) 0 0.53 1 0.24 2 0.11 3 0.04 4 0.02

Here, Sum of all probabilities is 0.94 which is not equal to 1.

Hence, This is not probability distribution.

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