Poisson distribution - class-XII
Description: poisson distribution | |
Number of Questions: 91 | |
Created by: Sundari Chatterjee | |
Tags: maths probability distributions probability distribution business maths random variables and probability distribution |
In a poisson distribution, the variance is $m$ . The sum of terms in odd places in the distribution is
lf the mean is $\lambda$ and the variance is $\sigma^{2}$ in a Poisson distribution, then
If the mean of P.D. is 5, then the variance of the same distribution is
If ${\overline{x}}$ and $\sigma^{2}$ are mean and variance of poisson distribution, then
The S.D. of poisson distribuition whose mean is $\lambda $ is
If the mean of Poisson distribution is $\displaystyle \frac{1}{2}$, then the ratio of $P(X=3)$ to $P(X=2)$ is
In a poisson distribution, the probability of $0$ success is $10$%. The mean of the distribution is equal to
The parameter $\lambda $ of poisson distribution is always
If X is a poisson variable with parameter 0.09,then its S.D. is
The standard deviation of P.D. is 1.5, then its mean is
If the mean of poisson distribution is $16$, then its S.D. is
Six coins are tossed $6400$ times. The probability of getting $6$ heads $x$ times using poison distribution is
A examinations consists of $8$ questions in each of which one of the $5$ alternatives is the correct one. On the assumption that a candidate who has done no preparatory work, chooses for each questions any one of the five alternatives with equal probability, then the probability that he gets more than one correct answer is equal to:
There are twenty bags each containing 10 bulbs and it is knows that no bag contains more than 5 defective bulbs and 3 bags have 5 defective bulbs. 4 bags have atleast 4 defective bulbs, 5 bags have atleast 3 defective bulbs, 6 bags have atleast 2 defective bulbs and 7 bags have atleast 1 defective bulb. Then the ratio of total defective bulbs is to non-defective bulbs is
For a Poission distribution which pair has same value.
For a poission distribution variable $X$ is such that $P(X = 2) = 9 P(X= 4) + 90 P(X= 6)$ the mean is
For a Poission distribution, which of the following is true
At a telephone enquiry system the number of phone calls regarding relevant enquiry follow Poisson distribution with a average of 5 phone calls during IO-minute time intervals. The probability that there is at the most one phone call during a 10-minute time period is
The probability of r successes in case of poissons distrbution is
A random variable $X$ has Poisson distribution with mean $2$. Then $P(X > 1.5)$ equals
If $X$ is a random poisson variate such that $\alpha =p(X=1)=p(X=2)$, then $p(X=4)=$
The variance of P.D. with parameter $\lambda $ is
If a random variable $X$ has a poisson distributionsuch that $P(X=1)=P(X=2)$, its mean and varianceare
If m is the variance of P.D., then the ratio of sum of the terms in even places to the sum of the terms in odd places is
If ${m}$ is the variance of Poisson distribution, then sum of the terms in even places is
If m is the variance of P.D., then the ratio of sum of the terms in odd places to the sum of the terms in even places is
A : the sum of the times in odd places in a P.D is $e^{-\lambda }$ cosh $\lambda$
R : cosh $\lambda =\frac{\lambda ^{1}}{1!}+\frac{\lambda ^{3}}{3!}+\frac{\lambda ^{5}}{5!}+......$
If $X$ is a poisson variate with $P(X=0)=P(X=1)$, then $P(X=2)$ is
If $X$ is a random poisson variate such that $E(X^{2})=6$, then $E(X)=$
For a Poisson variate $X$ if $P(X=2)=3P(X=3)$, then the mean of $X$ is
If $X$ is a poisson variate such that $P(X=0)=\dfrac{1}{2}$, the variance of $X$ is
If in a poisson frequency distribution, the frequency of $3$ successes is $\displaystyle \frac{2}{3}$ times the frequency of $4$ successes, the mean of the distribution is
If X is a poisson variate such that $P(X=2)=9p(X=4)+90p(X=6)$ , then the mean of x is
If $X$ is a poisson variate such that $P(X=0)=0.1,P(X=2)=0.2$, then the parameter $\lambda $
If $X$ is a poisson variate with $P(X=0) = 0.8,$ then the variance of $X$ is
If in a poisson distribution $P(X=1)=P(X=2)$; the mean of the distribution $f(x)=e^{-x}\dfrac{\lambda ^{x}}{\angle x}$ is
If for a poisson distribution $P(X=0)=0.2$, then the variance of the distribution is
In a Poisson distribution, the probability $P(X=0)$ is twice the probability $P(X=1)$. The mean of the distribution is
Suppose $X$ is a poisson variable such that $P(X=2)=\frac{2}{3}P(X=1)$, then $P(x=0)$ is
If $X$ is a poisson variable such that $P(X=2)=\frac{2}{3}P(X=1)$, then $P(x=3)$ is
If $X$ is a Poisson variate with parameter $1.5$, then $P(X>1)$ is
If $X$ is a poisson variate such that $P(X=0)=P(X=1)$,then $P(X=2)=$
A random variable $X$ follows poisson distribution such that $P(X=k)=P(X=k+1)$ then the parameter of the distribution $\lambda =$
In a poisson distribution $P(X=0)=P(X=1)=k$, then the value of $k$ is
If for a poisson variable $ X$, $P(X=1)=2.\ P(X=2)$, then the parameter $\lambda $ is
If $X$ is a Poisson variate such that $P(X=1) = P(X=2)$ then $P(X=4)=$
If a random variable $X$ follows a P.D. such that $P(X=1)=P(X=2)$, then $P(X=0)=$
If the first two terms of a Poisson distribution are equal to $k$, find $k$.
In a binomial distribution $n = 200, p = 0.04$. Taking Poisson distribution as an approximation to the binomial distribution .
Assertion (A) :- Mean of the Poisson distribution $= 8$
Reason (R) : In a Poisson distribution, $\displaystyle P(X=4)=\frac{512}{3e^{8}}$
If $X$ is a random poission variate such that $2P(X=0)+P(X=2)=2P(X=1)$ then $E(X)=$
If the probability of that a poisson variable $X$ takes a positive value $\geq 1$ is $1-e^{-1.5}$, then the varianceof the distribution is
In a town $10$ accidents take place in a span of $50$ days. Assuming that number of accidents follows Poisson distribution, the probability that there will be atleast one accident on a selected day at random is
A car hire firm has $2$ cars which it hires out day by day. If the number of demands for a car on each day follows Poisson distribution with parameter $1.5$, then the probability that both the cars is used is
If $X$ is a Poisson variate with parameter $\displaystyle \frac{3}{2}$, find $P(X\geq 2)$
If $X$ is a random Poisson variate such that $P(X=0)=\displaystyle\frac{1}{e}$, then the variance of the same distribution is
If on an average ,5 percent of the output in a factory making certain parts, is defective and that 200 units are in a package then the probability that atmost 4 defective parts may be found in that package is
Suppose $300$ misprints are distributed randomly throughout a book of $500$ pages. The probability that a given page contains, at least one misprint is
A manufactured product on an average has 2 defects per unit of product produced. If the number of defects follows Poisson distribution, the probability of finding at least one defect is
A car hire firm has $2$ cars which it hires out day by day. If the number of demands for a car on each day follows poisson distribution with parameter $1.5$, then the probability that only one car is used is
If $3$% of electric bulbs manufactured by a company are defective, the probability that a sample of $100$ bulbs has no defective bulbs is
On an average, a submarine on patrol sights $6$ enemy ships per hour. Assuming the number of ships sighted in a given length of time is a poisson variate, the probability of sighting atleast one ship in the next $15$ minutes is
If the number of telephone calls coming into a telephone exchange between 10 AM and 11 AM follows P.D. with parameter 2, then the probability of obtaining zero calls in that time interval is
A manufactured product on an average has $2$ defects per unit of product produced. If the number of defects follows P.D., the probability of finding zero defects is
If the number of telephone calls coming into a telephone exchange between 10 AM and 11 AM follows Poisson distribution with parameter 2 then the probability of obtaining at least one call in that time interval is
Cycle tyres are supplied in lots of $10$ and there is a chance of $1$ in $500$ to be defective. Using poisson distribution, the approximate number of lots containing no defectives in a consignment of $10,000$ lots if $e^{-0.02}=0.9802$ is
The chance of a traffic accident in a day attributed to a taxi driver is $0.001$. Out of a total of $1000$ days the number of days with no accident is
A manufacturer of cotter pins knows that $5$% of his product is defective. If he sells cotter pins in boxes of $100$ and guarantees that not more than $10$ pins will be defective, the approximate probability that a box will fail to meet the guaranteed quality is
The number of accidents in a year attributed to a taxi driver in a city follows Poisson distribution with mean $3$. Out of $1000$ taxi drivers, the approximate number of drivers with no accident in a year given that $e^{-3}=0.0498$ is
A manufacturing concern employing a large number of workers finds that, over a period of time, the average absentee rate is $2$ workers per shift. The probability that exactly $2$ workers will be absent in a chosen shift at random is
A manufacturer who produces medicine bottles finds that $0.1$% of the bottles are defective. The bottles are packed in boxes containing $500$ bottles. A drug manufacturer buys $100$ boxes from the producer of bottles. Using poisson distribution,the number of boxes with at least one defective bottle is
Suppose $2$% of the people on an average are left handed. The probability of 3 or more left handed among 100 people is
Suppose there is an average of $2$ suicides per year per $50,000$ population. In a city of population $1,00,000$, the probability that in a given year there are, zero suicides is
Suppose on an average $5$ out of $2000$ houses get damaged due to fire accident during summer. Out of $10,000$ houses in a locality, the probability that exactly $10$ houses will get damaged during summer is
A manufacturer who produces medicine bottles finds that $0.1$$\%$ of the bottles are defective. The bottles are packed in boxes containing $500$ bottles. A drug manufacturer buys $100$ boxes from the producer of bottles. Using Poisson distribution, the number of boxes with no defective bottle is
A company knows on the basis of past experience that $2$% of its blades are defective. The probability of having $3$ defective blades in a sample of $100$ blades if $e^{-2}=0.1353$ is
On the average a submarine on patrol sights $6$ enemy ships per hour. Assuming the number of ships sighted in a given length of time is a poisson variate, the probability of sighting $4$ ships in the next two hours is
Patients arrive randomly and independently at a Doctor's room from 8 AM at an average rate of one in 5 minutes. The waiting room can accommodate 12 persons. The probability that the room will be full when the doctor arrives at 9AM is
On an average, a submarine on patrol sights $6$ enemy ships per hour. Assuming the number of ships sighted in a given length of time is a Poisson variate, the probability of sighting at least two ships in the next $20$ minutes is
For a poisson distribution with parameter $\lambda = 0.25$, the value of the $2^{nd}$ moment about the origin is
If $X$ is a Poisson's variate such that $P(X=1)=3P(X=2)$, then find the variance of $X$.
If X is a random poisson variate such that $E(X^2)=6$, then $E(x)=$?
If $3 percent $ bulb manufactured by a company are defective; the probability that in a sample of $100$ bulbs exactly five defective is
If, in a Poisson distribution $P(X= 0)=k$ then the variance is:
The incidence of an occupational disease to the workers of a factory is found to be $\displaystyle \frac{1}{5000}$ . If there are $10,000$ workers in a factory then the probability that none of them will get the disease is
The probability that atmost $5$ defective fuses will be found in a box of $200$ fuses, if experience shows that $20 \%$ of such fuses are defective, is
There are $500$ boxes each containing $1000$ ballot papers for election. The chance that a ballot paper is defective is $0.002$. Assuming that the number of defective ballot papers follow Poisson distribution, the number of boxes containing at least one defective ballot paper given that $e^{-2}=0.1353$ is
Six unbiased coins are tossed $6400$ times. Using Poisson distribution, the approximate probability of getting six heads $2$ times is
A company knows on the basis of past experience that $2$% of the blades are defective. The probability of having 3 defective blades in a sample of $100$ blades is
A car hire firm has $2$ cars which it hires out day by day. If the number of demands for a car on each day follows poisson distribution with parameter $1.5$, then the probability that neither car is used is
In a big city, $5$ accidents take place over a period of $100$ days. If the numebr of accidents follows P.D., the probability that there will be $2$ accidents in a day is
If ${ \mu } _{ 2 }=20,{ \mu } _{ 2 }^{ 1 }=276$ for a discrete random variable $X$, then the mean of the random variable $X$ is