Statistics and Probability Answers

Consider a random process X(t) dened by

X(t) = U cos t + (V + 1) sin t; 􀀀-1 < t < 1

where U and V are independent r.v.'s for which

E[U] = E[V ] = 0; E[U2] = E[V 2] = 1

(a) Find the autocovariance function CX(t1; t2) of X(t).

(b) Is X(t) WSS?

The simplest error detection scheme used in data communication is parity checking.

Usually messages sent consist of characters, each character consisting of a number of

bits (a bit is the smallest unit of information and is either 1 or 0). In parity checking,

a 1 or 0 is appended to the end of each character at the transmitter to make the total

number of 1's even. The receiver checks the number of 1s in every character received,

and if the result is odd it signals an error. Suppose that each bit is received correctly

with probability 0.999, independently of other bits. What is the probability that a

7-bit character is received in error, but the error is not detected by the parity check?

(Hint: use the Binomial distribution)

The simplest error detection scheme used in data communication is parity checking.

Usually messages sent consist of characters, each character consisting of a number of

bits (a bit is the smallest unit of information and is either 1 or 0). In parity checking,

a 1 or 0 is appended to the end of each character at the transmitter to make the total

number of 1's even. The receiver checks the number of 1s in every character received,

and if the result is odd it signals an error. Suppose that each bit is received correctly

with probability 0.999, independently of other bits. What is the probability that a

7-bit character is received in error, but the error is not detected by the parity check?

(Hint: use the Binomial distribution)

The production department of WSS electronics wants to explore the relationships between the number of employees who assemble a certain product and the number of units produced per hour. The complete set of paired observations follows:

No. of employees: 2,4,6,8,5,12,10,9

Productions (units): 20,15,25,28,22,30,35,40

Q: Given Email B with its feature vector. Compute the probability of email B being “spam” and “ham” using Naïve bayes algorithm and then finally assign class label (spam or ham).

                                        P(spam) = 0.65

  Email B = < 0, 1, 1, 1 >, = < count(meeting), count(enron), count(dating), count(hi) >

       P (meeting | spam) = 0.6,                          P (meeting | ham) = 0.02

       P (enron | spam) = 0.4,                              P (enron | ham) = 0.001

       P (dating | spam) = 0.7,                             P (dating | ham) = 0.005

        P (hi | spam) = 0.3,                                   P (hi | ham) = 0.09