X, y , and z are three independent and uniformly distributed random variables be- tween zero and one. find the pdf of w = x + y + z. (hint: first find the pdf of v = x + y . the pdf of v should look like an isosceles triangle. then, find the pdf of w = v + z.)

Which of the following controllers anticipates the future from the slope of errors over time? a)-proportional b)-on/off c)-integral d)-derivative.

Refrigerant-134a enters the compressor of a refrigerator as superheated vapor at 0.14 mpa and -10°c at a rate of 0.05 ka/s and leaves at 0.8 mpa and 50°c. the refrigerant is cooied in the condenser to 0.72 mpa and 26'c. it is then throttled to 0.15 mpa. sketch the t-s diagram for the system and evaluate: 6) the rate of heat removai from the refrigerated space (kw), it) the power input to the compressor (kw), ii) the isentropic efficiency of the compressor (%), and iv) the cop of the refrigerator.

Aheavily insulated piston-cylinder device contains 0.02 m3 of steam at 300 kpa and 200 °c. 1.2 mpa. d this process. team is now compressed in a reversible manner to a pressure of etermine the entropy change and the work done on the steam during this process