$A$ 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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Similar Questions
$A$ random variable $X$ has the following probability distribution:
$X=x_i$ $-2$ $-1$ $0$ $1$ $2$ $P(X=x_i)$ $1/6$ $k$ $1/4$ $k$ $1/6$
The variance of this random variable is
| $X=x_i$ | $-2$ | $-1$ | $0$ | $1$ | $2$ |
| $P(X=x_i)$ | $1/6$ | $k$ | $1/4$ | $k$ | $1/6$ |
The variance of this random variable is
If the error involved in making a certain measurement is a continuous random variable $X$ with probability density function $f(x) = k(4 - x^2)$ for $-2 \leq x \leq 2$ and $f(x) = 0$ otherwise,then $P[-1 < X < 1] = $
State which of the following is not a probability distribution of a random variable. Give reasons for your answer.
$X$ $0$ $1$ $2$ $3$ $4$ $P(X)$ $0.1$ $0.5$ $0.2$ $-0.1$ $0.3$
| $X$ | $0$ | $1$ | $2$ | $3$ | $4$ |
| $P(X)$ | $0.1$ | $0.5$ | $0.2$ | $-0.1$ | $0.3$ |
Easy
View SolutionFind the probability distribution of the number of successes in two tosses of a die,where a success is defined as a number greater than $4$.
Medium
View SolutionThe p.m.f. of a random variable $X$ is given by $P(X=x) = \begin{cases} \frac{\binom{5}{x}}{2^5}, & x = 0, 1, 2, 3, 4, 5 \\ 0, & \text{otherwise} \end{cases}$. Then which of the following is not correct?
DifficultMHT CET 2024
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