State which of the following is not the probability distribution of a random variable. Give reasons for your answer.
$Y$ $-1$ $0$ $1$ $P(Y)$ $0.6$ $0.1$ $0.2$
| $Y$ | $-1$ | $0$ | $1$ |
| $P(Y)$ | $0.6$ | $0.1$ | $0.2$ |
(A) For a table to represent a probability distribution of a random variable $Y$,two conditions must be satisfied:
$1$. Each probability $P(Y_i)$ must be such that $0 \leq P(Y_i) \leq 1$.
$2$. The sum of all probabilities must be equal to $1$,i.e.,$\sum P(Y_i) = 1$.
In the given table:
Sum of probabilities $= 0.6 + 0.1 + 0.2 = 0.9$.
Since the sum of the probabilities is $0.9$,which is not equal to $1$,the given table does not represent a probability distribution of a random variable.
$1$. Each probability $P(Y_i)$ must be such that $0 \leq P(Y_i) \leq 1$.
$2$. The sum of all probabilities must be equal to $1$,i.e.,$\sum P(Y_i) = 1$.
In the given table:
Sum of probabilities $= 0.6 + 0.1 + 0.2 = 0.9$.
Since the sum of the probabilities is $0.9$,which is not equal to $1$,the given table does not represent a probability distribution of a random variable.
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