A tiny router has a queuing capacity to store 10 packets in its buffer. It has to drop any further packets arriving at it when its buffer is full. At every millisecond, the router either: i) sees an arrival with
probability 0:2, ii) completes forwarding of a packet with probability 0:6 (if its buffer is not empty; with
probability 0 otherwise), or iii) stays the same – no new arrival and no forwarding – with probability
0:2 (when the buffer is nonempty) or with probability 0:8 (when the buffer is empty).
Now determine the followings:
(a) The probability that the router has an empty buffer at any given millisecond.
(b) The probability that it has at least seven packets in its buffer at any given millisecond.

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?

(2, 4) (2, 1) (6, 12) (4, -5) (-2, 4) |(2, -4) (6, -12) (-4,5) quadrilateral abcd is reflected over the x-axis. quadrilateral abcd is translated 2 units right and 1 unit down. quadrilateral abcd is dilated by a scale factor of 3. quadrilateral abcd is rotated 180° clockwise about the origin. reset next

Atechnician compares repair costs for two types of microwave ovens (type i and type ii). he believes that the repair cost for type i ovens is greater than the repair cost for type ii ovens. a sample of 6767 type i ovens has a mean repair cost of $79.79$⁢79.79. the population standard deviation for the repair of type i ovens is known to be $19.18$⁢19.18. a sample of 5555 type ii ovens has a mean repair cost of $75.24$⁢75.24. the population standard deviation for the repair of type ii ovens is known to be $21.40$⁢21.40. conduct a hypothesis test of the technician's claim at the 0.050.05 level of significance. let μ1μ1 be the true mean repair cost for type i ovens and μ2μ2 be the true mean repair cost for type ii ovens. step 2 of 4 : compute the value of the test statistic. round your answer to two decimal places.