STATS 1L03 Lecture Notes - Lecture 20: Nipple

4. (10 marks) Use the intermediate value theorem and Rolle's theorem to show that the function f(x) = x+2 x2 +4x - 3 has exactly one root in the interval [0, 1]. Carefully explain your - work

The prior probabilities for events   are  . It is also known that  Suppose P(B | A1) = .20 and  

The prior probabilities for events    It is also known that    Suppose  .

Are events   mutually exclusive?

Compute  

Compute   

Compute P(B) (to 4 decimals).

Apply Bayes' theorem to compute   decimals).

Also apply Bayes' theorem to compute   (to 4 decimals).

4. Consider the function f(x) = 4x3 - 22 - 1 (c) [2 marks] Using the intermediate value theorem, prove that f(x) must have a root between 0 and 1.