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.)

Afoot bridge is made as a simple deck, 4 m long, with a cross section 2 m (wide) and 20 cm thick, and made of wood. the deck is supported at the two ends. the maximum load allowable on the bridge is 10 tons, provided it is uniformly distributed on the deck. to sense this load, a strain gauge is placed at the center of the bridge and its resistance is monitored. if the sensor has a nominal resistance of 350 s2 and a gauge factor of 3.6, what is the reading of the strain gauge at maximum load? the modulus of elasticity for the wood used in the construction is 10 gpa.