Microeconomic Theory
Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
Question
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Chapter 2, Problem 2.14P

(a)

To determine

The proof of E[g(x)]g[E(x)] (Jensen’s Inequality)

(b)

To determine

The proof of E[g(x)]g[E(x)]

(c)

To determine

The proof of E(x)=0[1F(x)]dx

(d)

To determine

The proof of P(xt)E(x)t (Markov’s Inequality)

(e)

To determine

  1. The proof that f(x)=2x3 for x1 is a proper PDF
  2. F(x) for this PDF
  3. E(x) for this PDF using the result of part (c)
  4. The proof that Markov’s inequality holds for this function

(f)

To determine

  1. The proof that f(x)=x23 for 1x2 is a proper PDF
  2. The value of E(x)
  3. The probability that 1x0
  4. The value of f(x|A) , where A is the event 0x2
  5. The value of E(x|A)
  6. Intuitive explanation of the results

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