Recent questions tagged poisson-distribution

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 $4$ $0$ $\Sigma_{i=0}^{\infty} i P(X=i+4)$ $\Sigma_{i=4}^{\infty} i P(X=i-4)$
Suppose $X$ and $Y$ are two independent random variables both following Poisson distribution with parameter $\lambda$. What is the value of $E(X-Y)^2$ ? $\lambda$ $2 \lambda$ $\lambda^2$ $4 \lambda^2$
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.....)$, then expected value of x is ....... 2 votes 1 answer 4 1 vote 1 answer 5 The second moment of a Poisson-distributed random variable is 2. The mean of the variable is .... My question on solving we get 2 values of lamda(ie mean) .One is -2 and the other is 1 .So which one to choose? 0 votes 1 answer 6 The second moment of a poisson distributed random variable is 2 the mean of the random variable is? 1 vote 1 answer 7 In this question if we do simply probability calculation then it is 8/20 40% but when I am appling poisson distribution then it is 40.4%. why we are getting two different answers?? 11 votes 2 answers 8 Suppose$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}$39 votes 4 answers 9 If a random variable$X$has a Poisson distribution with mean$5$, then the expectation$E\left [ \left ( x+2 \right )^{2} \right ]$equals ___. 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 _________ 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). 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. 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 &ndash; e^{-5}1 &ndash; e^{-10}$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$4 votes 1 answer 15 If the pdf of a Poisson distribution is given by$f(x) = \frac{e^{-2} 2^x}{x!}$then its mean is$2^x2-21$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}$22 votes 2 answers 17 Suppose$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})}\$