Steady-state temperatures (K) at three nodal points of a long rectangular rod are as shown. The rod experiences a uniform volumetric generation rate of 5 107 W/m3 and has a thermal conductivity of 20 W/mK. Two of its sides are maintained at a constant temperature of 300 K, while the others are insulated. (a) Determine the temperatures at nodes 1, 2, and 3. (b) Calculate the heat transfer rate per unit length (W/m) from the rod using the nodal temperatures. Compare this result with the heat rate calculated from knowledge of the volumetric generation rate and the rod dimensions

ENGR 3341 Probability Theory and Statistics Prof. Gelb Week 5 homework solutions Warm-up problems from textbook: Section 3.3 Problem 9: In this problem, we would like to show that the geometric random variable is memoryless. Let X ▯ Geometric(p). Show that P(X > m+ljX > m) = P(X > l); for m;l 2 f1;2;3;:::g We can interpret this in the following way: remember that a geometric random variable can be obtained by tossing a coin repeatedly until observing the ﬁrst heads. If we toss the coin several times and do not observe a heads, from now on it is like we start all over again. In other words, the failed coin tosses do not impact the distribution of waiting time from now on. The reason for this i