1. Bill s Barbershop has two barbers available to cut customers but Both barbers provide roughly the same experience and skill, but one is just a little bit slower than the other.

The version of Chebyshev's Inequality we saw in class states that a random variable X with expected value a = E(X) and standard deviation cr = Ml/(X) must satisfy {72 PilXPLEEElS 52 for any real number s > D. A common variation of Chebyshev's Inequality states that a random variable X with expected value ,a = E(X) and standard deviation :7 = V(X) must satisfy for any real number It > U. The two forms are equivalent let 5 = Ito to see why but the latter is often more convenient in statistics, where measuring the distance between X and ,u, in terms of a is likely to be pretty natural. Note that the second form is of interest 1 only if k > 1, since if k: 1: 1, then E 2 1 and any probability must be 3 1. 1. Given a xed real number k > 11 any xed real number a, and any xed real number a > 0, nd a probability density function 9(3) such that a continuous random variable X with this density will have E(X) = a, standard deviation V(X) = 0', and satisfy PtIXm 2 36(7):}612 [101 1. Bill's Barbershop has two barbers available to cut customers' hair. Both barbers provide roughly the same experience and skill, but one is just a little bit slower than the other. The process flow in Figure 5.90 shows that all customers go through Steps B1 and B2 and then can be served at either of the two barbers at Step B3. The process ends for all customers at Step B4. The numbers in parentheses indicate the minutes it takes that activity to process a customer. a. How long does it take the average customer to complete this process? b. What single activity is the bottleneck for the entire process? c. How many customers can this process serve in an hour?\fClient Work Center A ( days ) Work Center B ( days) A 5 7 B 7 8 C 4 H D 2 E 6 F 5 4\fWhy is it important to apply the inclusion and exclusion criteria when deciding which publications to include in a Systematic Review. llllodel solution: Students should discuss few of the foliowing', Date why is important in certain research studies Exposure of interest why did you sample the way you did, meaning choosing specically that population to sample from it Geographic location why is that location of particular interest Participants why did you choose specically those participants Reported outcomes {reports} usually this is secondary data Setting often, researchers look for a certain research setting, give an example or paint scenano Study design where populations are few, qualitative designs are preferred, give an example