The data in Exercise I were generated using the following functions. Use the polynomials constructed in Exercise 1 for the given value ofx to approximate f(x) and calculate the absolute error. a. f(x)=xlnx; approximate/(8.4). b. f(x) = sin(eA ' 2); approximate /(0.9). c. f(x) = x 3 + 4.00lx2 + 4.002x + 1.101; approximate /(-I/3). d. f(x) x cosx 2x2 + 3x I; approximate /(0.25).

Bayes Theorem Bayes Theorem Bayes Theorem P | A (A) If A and T are events, then: P |T P | AP(A) P T| A' (A') The events A and A’ form a partition of the sample space. This means • their union is the whole sample space and • the intersection of the two events A and A’ is empty. Bayes Theorem Given: P | B 0.3 P( ) 0.9 P(B’) = 1-0.9 P(A| B') 0.5 Find: P | A P B | A P | B (B) PA| B (B) P A|B' P(') PB | A 0.3(0.9) .84375 PB | A 0.8438 0.3(0.9) 0.5(0.1) Bayes Theorem Suppose that it snows in Greenland an av