State whether the given table is not the probability distributions of a random variable. Give reasons for your answer.
$\begin{matrix} x & 0 & 1 & 2 & 3 & 4 P (X) & 0.1 & 0.5 & 0.2 & - 0.1 & 0.3 \end{matrix}$

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Solution

It can be seen that for X = 3, P(X) = - 0.1
It is known that probability of any observation is not negative therefore, the given table is not a probability distribution of random variable

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State whether the given table is not the probability distributions of a random variable. Give reasons for your answer.
$\begin{matrix} Z & 3 & 2 & 1 & 0 & - 1 P (Z) & 0.3 & 0.2 & 0.4 & 0.1 & 0.05 \end{matrix}$

State whether the given table is not the probability distributions of a random variable. Give reasons for your answer.
$\begin{matrix} Y & - 1 & 0 & 1 P (Y) & 0.6 & 0.1 & 0.2 \end{matrix}$

State whether the given table is not the probability distributions of a random variable. Give reasons for your answer.
$\begin{matrix} X & 0 & 1 & 2 P (X) & 0.4 & 0.4 & 0.2 \end{matrix}$

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State which of the following are not the probability distributions of a random variable. Give reasons for your answer.

(i)

X	0	1	2
P (X)	0.4	0.4	0.2

(ii)

X	0	1	2	3	4
P (X)	0.1	0.5	0.2	− 0.1	0.3

(iii)

Y	−1	0	1
P (Y)	0.6	0.1	0.2

(iv)

Z	3	2	1	0	−1
P (Z)	0.3	0.2	0.4	0.1	0.05

Q. State which of the following are not the probability distributions of a random variable. Give reasons for your answer.

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State whether the given table is not the probability distributions of a random variable. Give reasons for your answer. x01234P(X)0.10.50.2−0.10.3

It can be seen that for X = 3, P(X) = - 0.1 It is known that probability of any observation is not negative therefore, the given table is not a probability distribution of random variable

State whether the given table is not the probability distributions of a random variable. Give reasons for your answer.
$\begin{matrix} x & 0 & 1 & 2 & 3 & 4 P (X) & 0.1 & 0.5 & 0.2 & - 0.1 & 0.3 \end{matrix}$

It can be seen that for X = 3, P(X) = - 0.1
It is known that probability of any observation is not negative therefore, the given table is not a probability distribution of random variable