Find the mean and variance of the r. v. X if it has p. m.f. P( 1) 0.2 = = X , P( 2) 0.3 = = X and P( 3) 0.5 = = X

Afour cylinder four-stroke in-line engine has a stroke of 160mm, connecting rod length of 150mm, a reciprocating mass of 3kg and its firing order is 1-3-4-2. the spacing between cylinders is 100mm. i. show that the engine is in balance with regard to the primary inertia forces and primary 3. a and secondary inertia couples. li determine the out of balance secondary inertia force ii. propose ways of balancing this out of balance force and discuss the challenges that will arise

Thermal stresses are developed in a metal when its a) initial temperature is changed b) final temperature is changed c) density is changed d) thermal deformation is prevented e) expansion is prevented f) contraction is prevented

Carbon dioxide gas expands isotherm a turbine from 1 mpa, 500 k at 200 kpa. assuming the ideal gas model and neglecting the kinetic and potential energies, determine the change in entropy, heat transfer and work for each kilogram of co2.