The number of packets received at a router input during an interval of duration t seconds is modeled by a Poisson random variable. The probability of arriving k packets in the interval is where parameter β is the packet arrival rate, measured in packets/second. a)Write the equation of the probability density function of the random variable of Poisson .

b)Show that the arrival time between packets T is in this case an exponential random variable and determine the value of the parameter.

c)If the packets arrive with an equal speed of 2048 kilobits/second and the packet size is equal to 1024 bits determine the value of β.

d)Determine the value of the duration t of the observation interval so that the probability of no packet arriving is greater than 0.9.

e)Determine the duration t value of the observation interval so that the probability of arriving at least one packet is greater than 0.9.

The means and mean absolute deviations of the individual times of members on two 4x400-meter relay track teams are shown in the table below. means and mean absolute deviations of individual times of members of 4x400-meter relay track teams team a team b mean 59.32 s 59.1 s mean absolute deviation 1.5 s 245 what percent of team b's mean absolute deviation is the difference in the means? 9% 15% 25% 65%

High school seniors with strong academic records apply to the nation’s most selective colleges in greater numbers each year. because the number of slots remains relatively stable, some colleges reject more early applicants. suppose that for a recent admissions class, an ivy league college received 2851 applications for early admission. of this group, it admitted 1033 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. in the past, this school has admitted 18% of the deferred early admission applicants during the regular admission process. counting the students admitted early and the students admitted during the regular admission process, the total class size was 2375. let e, r, and d represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool.suppose a student applies for early admission. what is the probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process?

5. (03.02)if g(x) = x2 + 3, find g(4). (2 points)1619811