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.

To determine the number of deer in a forest a forest ranger tags 280 and releases them back

You are designing a rectangular pet pen for your new baby puppy. you have 30 feet of fencing you would like the fencing to be 6 1/3 feet longer than the width

Design an er diagram for keeping track of information about votes taken in the u.s. house of representatives during the current two-year congressional session. the database needs to keep track of each u.s. state's name (e.g., texas', new york', california') and include the region of the state (whose domain is {northeast', midwest', southeast', southwest', west'}). each congress person in the house of representatives is described by his or her name, plus the district represented, the start date when the congressperson was first elected, and the political party to which he or she belongs (whose domain is {republican', democrat', 'independent', other'}). the database keeps track of each bill (i.e., proposed law), including the bill name, the date of vote on the bill, whether the bill passed or failed (whose domain is {yes', no'}), and the sponsor (the congressperson(s) who sponsored - that is, proposed - the bill). the database also keeps track of how each congressperson voted on each bill (domain of vote attribute is {yes', no', abstain', absent'}). additional information: