In the homework, you were asked to give an example of a sequence with more than

Question

In the homework, you were asked to give an example of a sequence with more than one cluster point. Give an example of a sequence with infinitely many cluster points. A plane takes off from Binghamton airport traveling in a random direction, chosen uniformly between 0 and 360 degrees. The plane does not deviate to the left or right, and travels in a great circle, ultimately returning to Binghamton after flying around the Earth. Estimate the probability that the plane passes over Australia. Make (and state) whatever assumptions are necessary to answer the question, and explain how you got your answer. An unknown combinational circuit has two inputs, and one output. (a) how many different combinational circuits are possible? Two circuits are considered the same if they have the same truth table. (b) Suppose one such circuit is chosen randomly, each possibility equally likely to occur. You observe that if both inputs to the circuit are TRUE, the output is TRUE. Knowing this, what is the probability that the unknown circuit is equivalent to an AND gate? Let U and V be independent random variables uniformly distributed over [0, 1]. Write the cdf, pdf, expected value and variance of Z = U + V. Give an example of a random variable X where EX = 0 and Var[X] = 1, but E|X| = 1 and Var [|X|] = 0. |X| denotes the absolute value of X. A random variable Y varies over the interval [0, 1] and has a pdf given by f_Y (a) = C sin^2 (2 pi a) .. where C is some constant. (a) Find C. (b) Compute the mean and variance of Y.

Explanation / Answer

some problems are from other subjects.I am giving the solution of 5 which is from statistics

Let X takes values -1 and 1 with probability .5 and .5

Hence E(X)=0

V(X)=1

E(MOD(X))=1

V(MOD(X))=0

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