Let X be a random variable with density function:

f(x) = x if x ∈ (0, 1]

2 − x if x ∈ (1, 2]

0 the rest

Determine the distribution and density functions of the random variables:

a) Y = X + 1;

b) Y = −1/2X;

c) Y = X^2;

Heat is added to a piston-cylinder device filled with 2 kg of air to raise its temperature 400 c from an initial temperature of t1 27 cand pressure of pi 1 mpa. the process is isobaric process. find a)-the final pressure p2 b)-the heat transfer to the air.

Afull journal bearing has a journal diameter of 27 mm, with a unilateral tolerance of -0.028 mm. the bushing bore has a diameter of 27.028 mm and a unilateral tolerance of 0.04 mm. the l/d ratio is 0.5. the load is 1.3 kn and the journal runs at 1200 rev/min. if the average viscosity is 50 mpa-s, find the minimum film thickness, the power loss, and the side flow for the minimum clearance assembly.

How to increase the thermal officiency of an ideal simple rankino cycle? among these methods, which one is the best and why?