Which of the following cannot be a valid assignment of probabilities for outcomes of sample space $S = \{\omega_{1}, \omega_{2}, \omega_{3}, \omega_{4}, \omega_{5}, \omega_{6}, \omega_{7}\}$?
Outcome $\omega_{1}$ $\omega_{2}$ $\omega_{3}$ $\omega_{4}$ $\omega_{5}$ $\omega_{6}$ $\omega_{7}$ Probability $-0.1$ $0.2$ $0.3$ $0.4$ $-0.2$ $0.1$ $0.3$
| Outcome | $\omega_{1}$ | $\omega_{2}$ | $\omega_{3}$ | $\omega_{4}$ | $\omega_{5}$ | $\omega_{6}$ | $\omega_{7}$ |
| Probability | $-0.1$ | $0.2$ | $0.3$ | $0.4$ | $-0.2$ | $0.1$ | $0.3$ |
- AThe assignment is valid.
- BThe assignment is invalid because probabilities are negative.
- CThe assignment is invalid because the sum of probabilities is not $1$.
- DThe assignment is invalid because the number of outcomes is $7$.
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State which of the following is not a probability distribution of a random variable. Give reasons for your answer.
$X$ $0$ $1$ $2$ $3$ $4$ $P(X)$ $0.1$ $0.5$ $0.2$ $-0.1$ $0.3$
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Easy
View Solution$A$ person plays a game of tossing a coin thrice. For each head,he is given $Rs. 2$ by the organiser of the game and for each tail,he has to give $Rs. 1.50$ to the organiser. Let $X$ denote the amount gained or lost by the person. Show that $X$ is a random variable and exhibit it as a function on the sample space of the experiment.
Medium
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