For the following sequential circuit, the table gives the contents of the PLA. (All PLA outputs are 0 for input combinations not listed in the table.) (a) Construct a transition table and draw a state graph. (b) Draw a timing diagram showing the clock, X, Q1, Q2, and Z for the input sequence X = 10011. Assume that initially Q1 = Q2 = 0. (c) Identify any false outputs in the timing diagram. What is the correct output sequence for Z?

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