The number of persons joining a cinema ticket counter in a minute follows a Poisson distribution with parameter $\lambda = 6$. The probability that at least one and at most five persons join the queue in a particular minute is:
- A$e^{-6 \times 6}(25.48)$
- B$e^{-6}\left(\frac{6}{2}+\frac{6^3}{3 !}+\frac{6^4}{4 !}\right)$
- C$6 \times e^{-6}(29.8)$
- D$e^{-6}\left(6+\frac{6^2}{2}+\frac{6^3}{3 !}+\frac{6^4}{4 !}\right)$
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Similar Questions
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 | $-0.1$ | $0.2$ | $0.3$ | $0.4$ | $-0.2$ | $0.1$ | $0.3$ |
Easy
View SolutionThe probability distribution of a random variable $X$ is given below:
$X$ $1$ $2$ $3$ $4$ $5$ $6$ $P(X=x_i)$ $\alpha$ $\alpha$ $\alpha$ $\beta$ $\beta$ $0.3$
If $\mu$ and $\sigma^2$ represent the mean and variance of $X$ and $\mu=4.2$,then $\sigma^2+\mu^2=$
| $X$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ |
| $P(X=x_i)$ | $\alpha$ | $\alpha$ | $\alpha$ | $\beta$ | $\beta$ | $0.3$ |
If $\mu$ and $\sigma^2$ represent the mean and variance of $X$ and $\mu=4.2$,then $\sigma^2+\mu^2=$
The range of a random variable $X$ is $\{1, 2, 3, \ldots\}$ and $P(X=x) = \frac{c^x}{x!}$ for $x = 1, 2, 3, \ldots$. Then the value of $c$ is
The probability distribution of a discrete random variable $X$ is given by the following table:
$X$ $1$ $2$ $3$ $4$ $5$ $6$ $P(X)$ $K$ $2K$ $3K$ $4K$ $5K$ $6K$
Find the value of $P(2 < X < 6)$.
| $X$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ |
|---|---|---|---|---|---|---|
| $P(X)$ | $K$ | $2K$ | $3K$ | $4K$ | $5K$ | $6K$ |
Find the value of $P(2 < X < 6)$.
$A$ coin is tossed twice in succession. Let $X$ represent the number of tails in two tosses,then the probability distribution of $X$ is given by
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