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Recent questions tagged poisson-distribution

2 votes
1 answer
1
The number of cars $(X)$ arriving at a service station per day follows a Poisson distribution with mean $4$. The service station can provide service to a maximum of $4$ cars per day. Then the expected number of cars that do not get service per day equals $4$ $0$ $\Sigma_{i=0}^{\infty} i P(X=i+4)$ $\Sigma_{i=4}^{\infty} i P(X=i-4)$
asked Sep 23, 2019 in Probability Arjun 488 views
0 votes
2 answers
2
Suppose $X$ and $Y$ are two independent random variables both following Poisson distribution with parameter $\lambda$. What is the value of $E(X-Y)^2$ ? $\lambda$ $2 \lambda$ $\lambda^2$ $4 \lambda^2$
asked Sep 13, 2018 in Probability jothee 281 views
2 votes
0 answers
3
If x has a modified Poisson distribution $P_k = P_r(x = k) =$\Large \frac{ ( e^m - 1 )^{-1} m^k}{k!}$, $(k = 1,2,3.....)$, then expected value of x is .......
asked Aug 31, 2018 in Probability Mk Utkarsh 346 views
1 vote
1 answer
5
The second moment of a Poisson-distributed random variable is 2. The mean of the variable is .... My question on solving we get 2 values of lamda(ie mean) .One is -2 and the other is 1 .So which one to choose?
asked Nov 23, 2017 in Mathematical Logic Kalpataru Bose 2.3k views
0 votes
1 answer
6
The second moment of a poisson distributed random variable is 2 the mean of the random variable is?
asked Aug 20, 2017 in Probability saumya mishra 289 views
1 vote
1 answer
7
11 votes
2 answers
8
Suppose $X$ is distributed as Poisson with mean $λ.$ Then $E(1/(X + 1))$ is $\frac{e^{\lambda }-1}{\lambda }$ $\frac{e^{\lambda }-1}{\lambda +1}$ $\frac{1-e^{-\lambda }}{\lambda}$ $\frac{1-e^{-\lambda }}{\lambda + 1}$
asked May 11, 2017 in Probability neha.i 1.4k views
39 votes
4 answers
9
If a random variable $X$ has a Poisson distribution with mean $5$, then the expectation $E\left [ \left ( x+2 \right )^{2} \right ]$ equals ___.
asked Feb 14, 2017 in Probability Kantikumar 9.5k views
3 votes
0 answers
10
If two cards are drawn from a pack of 52 cards, which are diamonds. Using Poissons distribution find the probability of getting two diamonds at least 3 times in 51 consecutive trials of two cards drawing each time _________
asked Jan 19, 2017 in Probability Supremo 594 views
3 votes
1 answer
11
$P_{n} (t)$ is the probability of $n$ events occurring during a time interval $t$. How will you express $P_{0} (t + h)$ in terms of $P_{0} (h)$, if $P_{0} (t)$ has stationary independent increments? (Note: $P_{t} (t)$is the probability density function).
asked Nov 30, 2016 in Probability makhdoom ghaya 455 views
5 votes
1 answer
12
Which of the following statements are FALSE? For poisson distribution, the mean is twice the variance. In queuing theory, if arrivals occur according to poisson distribution, then the inter-arrival time is exponentially distributed. The distribution of waiting ... the time between successive arrivals is exponential, then the time between the occurences of every third arrival is also exponential.
asked Nov 27, 2016 in Probability makhdoom ghaya 1k views
2 votes
1 answer
13
The multiuser operating system, $20$ requests are made to use a particular resource per hour, on an average the probability that no request are made in $45$ minutes is $e^{-15}$ $e^{-5}$ $1 – e^{-5}$ $1 – e^{-10}$
asked Aug 18, 2016 in Probability makhdoom ghaya 2.6k views
3 votes
1 answer
14
In a aloha implemented shared channel probability of transmission of a station in a time span of T is p. Given, probability such that NO station transmit in a time duration of $2T$ is $50\%$ , where T = one frame transmission time. What is the value of p is if total no of station = $100$
asked Jul 11, 2016 in Computer Networks dd 500 views
4 votes
1 answer
15
If the pdf of a Poisson distribution is given by $f(x) = \frac{e^{-2} 2^x}{x!}$ then its mean is $2^x$ $2$ $-2$ $1$
asked Jun 15, 2016 in Probability jothee 1.9k views
28 votes
1 answer
16
In a multi-user operating system on an average, $20$ requests are made to use a particular resource per hour. The arrival of requests follows a Poisson distribution. The probability that either one, three or five requests are made in $45$ minutes is given by : $6.9 \times 10^6 \times e^{-20}$ $1.02 \times 10^6 \times e^{-20}$ $6.9 \times 10^3 \times e^{-20}$ $1.02 \times 10^3 \times e^{-20}$
asked Oct 30, 2014 in Probability Ishrat Jahan 5k views
22 votes
2 answers
17
Suppose $p$ is the number of cars per minute passing through a certain road junction between $5$ PM and $6$ PM, and $p$ has a Poisson distribution with mean $3$. What is the probability of observing fewer than $3$ cars during any given minute in this interval? $\dfrac{8}{(2e^{3})}$ $\dfrac{9}{(2e^{3})}$ $\dfrac{17}{(2e^{3})}$ $\dfrac{26}{(2e^{3})}$
asked Aug 7, 2014 in Probability gatecse 5.7k views
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