Hi Dear
I need you help to answer theses questions if you don't mind
Plz PLZ
1. A unbiased die is thrown once. Compute the probability of the following events.
a). The number of spots shown is odd.
b). The number of spots shown is less than 3.
c). The number of spots shown is a prime number.
2. A prisoner in a Kafkaesque prison is put in the following situation. A regular deck of
52 cards is placed in front of him. He must choose cards one at a time, and once a
card is chosen, the card is replaced in the deck and the deck is shuffled. If the prisoner
happens to select three consecutive red cards, he is executed. If he happens to selects
6 cards before three consecutive red cards appear he is granted freedom. What is the
probability that the prisoner is executed.
3. Three marksmen fire simultaneously and independently at a target. What is the
probability of the target being hit at least once, given that marksman one hits a target
9 times out of 10, marksman two hits a target 8 times out of 10 while marksman three
only hits a target 1 out of every 2 times.
4. Calculate the expected value and variance of a random variable that follows the
exponential distribution with parameter λ.
5. Calculate the expected value and variance of a random variable that follows the
Poisson distribution with parameter λ.
6. Jobs to be performed on a machine arrive according to a Poisson distribution with a
rate of two per hour. Suppose that the machine breaks down from time to time and it
takes 1 hour to be repaired. What is the probability that a) zero, b) two, and c) five
new jobs will arrive during this time?
7. SSI chips, essential to the running of a computer system, fail in accordance with a
Poisson distribution at the rate of one chip per five weeks. If there are two spare chips
on hand and if a new supply will arrive in eight weeks, what is the probability that
during the next eight weeks the system will be down for a week or more owing to
lack of chips?
8. Jobs arrive to a computer system have been found to require a CPU time that can be
modelled by an exponential distribution with mean 140 msec. The CPU scheduling
algorithm is quantum-oriented so that a job not completing within a quantum of 100
msec will be routed back to the tail of the queue of waiting jobs.
a). What is the probability that an arriving job will be forced to wait for a second
quantum?
b). Of the 800 jobs coming during a day, how many are expected to finish within the
first quantum?
