(A) The Poisson distribution is given by the formula $P(X=r) = \frac{e^{-m} m^r}{r!}$,where $m$ is the mean number of occurrences.Given $m = 5$,we wan

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(A) The Poisson distribution is given by the formula $P(X=r) = \frac{e^{-m} m^r}{r!}$,where $m$ is the mean number of occurrences.Given $m = 5$,we want to find the probability of at most one phone call,which is $P(X \leq 1) = P(X=0) + P(X=1)$.For $r=0$: $P(X=0) = \frac{e^{-5} 5^0}{0!} = e^{-5}$.For $r=1$: $P(X=1) = \frac{e^{-5} 5^1}{1!} = 5e^{-5}$.Adding these probabilities: $P(X \leq 1) = e^{-5} + 5e^{-5} = 6e^{-5}$.

Class 12 Mathematics Probability Probability distribution

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At a telephone enquiry system,the number of phone calls regarding relevant enquiries follows a Poisson distribution with an average of $5$ phone calls during $10$-minute time intervals. The probability that there is at most one phone call during a $10$-minute time period is:

AIEEE 2006 All AIEEE

A
$6e^{-5}$
B
$5e^{-5}$
C
$e^{-5}$
D
$4e^{-5}$

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The following table shows the probability distribution of smart phones sold in a shop per day:
Number of smart phones $(x)$ $0$ $1$ $2$ $3$ $4$ $5$
Probability $(P(x))$ $k$ $0.3$ $0.15$ $0.15$ $0.1$ $2k$

Then $E(x) = ?$

Number of smart phones $(x)$	$0$	$1$	$2$	$3$	$4$	$5$
Probability $(P(x))$	$k$	$0.3$	$0.15$	$0.15$	$0.1$	$2k$

EasyMHT CET 2022

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Suppose the number of accidents occurring on a highway in each day follows a Poisson random variable with parameter $3$. Then,what is the probability that no accidents occur today?

DifficultAP EAMCET 2020

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For a Poisson variate $X$,if $P(X=2)=3 P(X=3)$,then the mean of $X$ is:

DifficultAP EAMCET 2003

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The probability distribution of a random variable $X$ is given by:
$X = x_i$ $0$ $1$ $2$ $3$ $4$
$P(X = x_i)$ $0.4$ $0.3$ $0.1$ $0.1$ $0.1$

Then the variance of $X$ is:

$X = x_i$	$0$	$1$	$2$	$3$	$4$
$P(X = x_i)$	$0.4$	$0.3$	$0.1$	$0.1$	$0.1$

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Suppose that a book of $600$ pages contains $40$ print mistakes. Assume that these errors are randomly distributed throughout the book and the number of errors per page follows a Poisson distribution. The probability that all the $10$ pages selected at random have no print mistakes is

MediumAP EAMCET 2022

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At a telephone enquiry system,the number of phone calls regarding relevant enquiries follows a Poisson distribution with an average of $5$ phone calls during $10$-minute time intervals. The probability that there is at most one phone call during a $10$-minute time period is:

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The following table shows the probability distribution of smart phones sold in a shop per day:Number of smart phones $(x)$$0$$1$$2$$3$$4$$5$Probability $(P(x))$$k$$0.3$$0.15$$0.15$$0.1$$2k$Then $E(x) = ?$

Suppose the number of accidents occurring on a highway in each day follows a Poisson random variable with parameter $3$. Then,what is the probability that no accidents occur today?

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The following table shows the probability distribution of smart phones sold in a shop per day:
Number of smart phones $(x)$ $0$ $1$ $2$ $3$ $4$ $5$
Probability $(P(x))$ $k$ $0.3$ $0.15$ $0.15$ $0.1$ $2k$

Then $E(x) = ?$

The probability distribution of a random variable $X$ is given by:
$X = x_i$ $0$ $1$ $2$ $3$ $4$
$P(X = x_i)$ $0.4$ $0.3$ $0.1$ $0.1$ $0.1$

Then the variance of $X$ is: