$A$ service station manager sells gas at an average of ₹ $100$ per hour on a rainy day,₹ $150$ per hour on a dubious day,₹ $250$ per hour on a fair day,and ₹ $300$ per hour on a clear sky day. If weather bureau statistics show the probabilities of weather as follows,then his mathematical expectation is:
Weather Clear Fair Dubious Rainy Probability $0.50$ $0.30$ $0.15$ $0.05$
| Weather | Clear | Fair | Dubious | Rainy |
| Probability | $0.50$ | $0.30$ | $0.15$ | $0.05$ |
- A$257.5$
- B$252.5$
- C$250$
- D$247.5$
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$A$ fair coin is tossed four times. $A$ person wins $Rs. 1$ for each head and loses $Rs. 1.50$ for each tail that turns up. From the sample space,calculate the different amounts of money one can have after four tosses and the probability of having each of these amounts.
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$A$ random variate $X$ takes the values $0, 1, 2, 3$ and its mean is $1.3$. If $P(X=3) = 2 P(X=1)$ and $P(X=2) = 0.3$,then $P(X=0)$ is equal to:
DifficultTS EAMCET 2003
View SolutionIf a discrete random variable $X$ has the probability distribution as follows:
$X = x$ $0$ $1$ $2$ $3$ $P(X = x)$ $k$ $3k$ $3k$ $k$
Then $Var(X) = $
| $X = x$ | $0$ | $1$ | $2$ | $3$ |
| $P(X = x)$ | $k$ | $3k$ | $3k$ | $k$ |
Then $Var(X) = $
Let a sample space be $S = \{\omega_{1}, \omega_{2}, \ldots, \omega_{6}\}$. Which of the following assignments of probabilities to each outcome is valid?
Outcome Probability $\omega_{1}$ $\frac{1}{12}$ $\omega_{2}$ $\frac{1}{12}$ $\omega_{3}$ $\frac{1}{6}$ $\omega_{4}$ $\frac{1}{6}$ $\omega_{5}$ $\frac{1}{6}$ $\omega_{6}$ $\frac{3}{2}$
| Outcome | Probability |
| $\omega_{1}$ | $\frac{1}{12}$ |
| $\omega_{2}$ | $\frac{1}{12}$ |
| $\omega_{3}$ | $\frac{1}{6}$ |
| $\omega_{4}$ | $\frac{1}{6}$ |
| $\omega_{5}$ | $\frac{1}{6}$ |
| $\omega_{6}$ | $\frac{3}{2}$ |
Easy
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