State which of the following is not a probability distribution of a random variable. Give reasons for your answer.
$X$ $0$ $1$ $2$ $3$ $4$ $P(X)$ $0.1$ $0.5$ $0.2$ $-0.1$ $0.3$
| $X$ | $0$ | $1$ | $2$ | $3$ | $4$ |
| $P(X)$ | $0.1$ | $0.5$ | $0.2$ | $-0.1$ | $0.3$ |
(N/A) probability distribution of a random variable must satisfy two conditions:
$1$. $P(X) \ge 0$ for all values of $X$.
$2$. $\sum P(X) = 1$.
In the given table,for $X = 3$,the value of $P(X)$ is $-0.1$.
Since the probability of any event cannot be negative,the condition $P(X) \ge 0$ is violated.
Therefore,the given table is not a probability distribution of a random variable.
$1$. $P(X) \ge 0$ for all values of $X$.
$2$. $\sum P(X) = 1$.
In the given table,for $X = 3$,the value of $P(X)$ is $-0.1$.
Since the probability of any event cannot be negative,the condition $P(X) \ge 0$ is violated.
Therefore,the given table is not a probability distribution of a random variable.
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