$X~Po\left(1.5\right)$. Calculate: $P\left(X=4\right)$

Important Questions on The Poisson Distribution

EASY

Mathematics (9709)>P-6: Statistics and Probability 2>The Poisson Distribution>Poisson Probability Distribution

If the number of incoming buses per minute at a bus terminus is a random variable having a Poisson distribution with $\lambda =0.9$, find the probability that there will be : at least $14$ incoming buses during a period of $11$ minutes.

MEDIUM

Mathematics (9709)>P-6: Statistics and Probability 2>The Poisson Distribution>Poisson Probability Distribution

If, in a Poisson distribution $P(X=0)=k$ then the variance is 

EASY

Mathematics (9709)>P-6: Statistics and Probability 2>The Poisson Distribution>Poisson Probability Distribution

If the number of incoming buses per minute at a bus terminus is a random variable having a Poisson distribution with $\lambda =0.9$, find the probability that there will be : exactly $9$ incoming buses during a period of $5$ minutes.

MEDIUM

Mathematics (9709)>P-6: Statistics and Probability 2>The Poisson Distribution>Poisson Probability Distribution

In poisson distribution which of the following is same?

MEDIUM

Mathematics (9709)>P-6: Statistics and Probability 2>The Poisson Distribution>Poisson Probability Distribution

If $X$ is a Poisson variate such that $2P(X=1)=5P(X=5)+2P(X=3),$ then the standard deviation of $X$ is

MEDIUM

Mathematics (9709)>P-6: Statistics and Probability 2>The Poisson Distribution>Poisson Probability Distribution

Let $X$ be a Poisson random variable with a parameter $\lambda .$ Then the probability that $X$ is odd is: 

EASY

Mathematics (9709)>P-6: Statistics and Probability 2>The Poisson Distribution>Poisson Probability Distribution

If the number of incoming buses per minute at a bus terminus is a random variable having a Poisson distribution with $\lambda =0.9$, find the probability that there will be : fewer than $10$ incoming buses during a period of $8$ minutes.

MEDIUM

Mathematics (9709)>P-6: Statistics and Probability 2>The Poisson Distribution>Poisson Probability Distribution

If $S$ is a Poisson variate such that $P\left(x=1\right)=0.7,P\left(x=2\right)=0.3$, then $P\left(x=0\right)$______.

EASY

Mathematics (9709)>P-6: Statistics and Probability 2>The Poisson Distribution>Poisson Probability Distribution

If the probability that an individual will suffer a bad reaction from an injection is $0.001,$ then the probability that out of $2000$ individuals, exactly $3$ individuals suffer a bad reaction is

EASY

Mathematics (9709)>P-6: Statistics and Probability 2>The Poisson Distribution>Poisson Probability Distribution

If '$m$' is the mean of a Poisson distribution, then $P\left(x>0\right)=$

EASY

Mathematics (9709)>P-6: Statistics and Probability 2>The Poisson Distribution>Poisson Probability Distribution

If the parameter of poisson distribution is m and $\left(\mathrm{mean}+\mathrm{S}.\mathrm{D}.=\frac{6}{25}\right)$ then find $m$.

HARD

Mathematics (9709)>P-6: Statistics and Probability 2>The Poisson Distribution>Poisson Probability Distribution

Let $p\left(x\right)$ represent the probability mass function of a Poisson distribution. If its mean $\lambda =3.725,$ then value of $x$ at which $p\left(x\right)$ is maximum is

EASY

Mathematics (9709)>P-6: Statistics and Probability 2>The Poisson Distribution>Poisson Probability Distribution

Which one of the following has Poisson distribution?

EASY

Mathematics (9709)>P-6: Statistics and Probability 2>The Poisson Distribution>Poisson Probability Distribution

A Poisson variable satisfies $P(X=1)=P(X=2)$. Find $P\left(X=5\right)$

EASY

Mathematics (9709)>P-6: Statistics and Probability 2>The Poisson Distribution>Poisson Probability Distribution

Which of the following is uni-parametric distribution?

MEDIUM

Mathematics (9709)>P-6: Statistics and Probability 2>The Poisson Distribution>Poisson Probability Distribution

A die is thrown twice. If getting a number greater than four on the die is considered a success, then the variance of the probability distribution of the number of successes is

EASY

Mathematics (9709)>P-6: Statistics and Probability 2>The Poisson Distribution>Poisson Probability Distribution

If $6$ is the mean of a Poisson distribution, then $P\left(X\ge 3\right)=$

EASY

Mathematics (9709)>P-6: Statistics and Probability 2>The Poisson Distribution>Poisson Probability Distribution

Face masks are supplied to a junior college in packets of $100.$ If there is a chance that $1$ in $500$ face mask is defective, then the number of packets containing no defective face masks in a consignment of $10,000$ packets, is

MEDIUM

Mathematics (9709)>P-6: Statistics and Probability 2>The Poisson Distribution>Poisson Probability Distribution

In a communication network, ninety-eight percent of messages are transmitted with no error. If a random variable $X$ denotes the number of incorrectly transmitted messages, then the probability that atmost one message is transmitted incorrectly out of 500 messages sent, is

EASY

Mathematics (9709)>P-6: Statistics and Probability 2>The Poisson Distribution>Poisson Probability Distribution

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?