Question: Let N be a nonnegative, integer-valued random variable. Show that P{N >0} (E[N])2 E[N2] and explain how this inequality can be used to derive

Let N be a nonnegative, integer-valued random variable. Show that P{N >0}  (E[N])2 E[N2]

and explain how this inequality can be used to derive additional bounds on a reliability function.

Hint:

E[N2] = E[N2 |N >0]P{N >0} (Why?)

 (E[N |N >0])2P{N >0} (Why?)

Now multiply both sides by P{N >0}.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Theory Of Probability Questions!

Q:

Problem 13.18 and Exhibit 13.7 in Chapter 13 present selected hypothetical data from projected financial statements for Steak 'n Shake for Year +1 to Year +11. The amounts for Year +11 reflect a...

Q:

Please help me with the attached article review. I have attached the instructions as well as the scholarly article to use. The topic is Time Value of Money Analysis. Time value of money analysis...

Q:

Consider the trigonometric series a0 2 + X r=1 (ar cos rx + br sin rx) where a0, a1, a2, . . . and b1, b2, . . . are constants and suppose that f(x) is a periodic function of x with period 2. (a)...

Q:

QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...

Q:

17. Let N be a nonnegative, integer-valued random variable. Show that P{N > 0} > (E[N]) E[N2] and explain how this inequality can be used to derive additional bounds on a reliability function. Hint:...

Q:

17. Let N be a nonnegative, integer-valued random variable. Show that P{N > 0} (E[N])2 E[N2] and explain how this inequality can be used to derive additional bounds on a reliability function. Hint:...

Q:

Let N be a nonnegative, integer-valued random variable. Show that P{N > 0} (E[N])2 E[N2] and explain how this inequality can be used to derive additional bounds on a reliability function. Hint: E[N2]...

Q:

17. Let N be a nonnegative, integer-valued random variable. Show that P{N > 0} (E[N])2 E[N2] and explain how this inequality can be used to derive additional bounds on a reliability function. Hint:...

Q:

17. Let N be a nonnegative, integer-valued random variable. Show that P{N > 0} (E[N])2 E[N2] and explain how this inequality can be used to derive additional bounds on a reliability function.

Q:

17. Let N be a nonnegative, integer-valued random variable. Show that and explain how this inequality can be used to derive additional bounds on a reliability function. Hint: E[N2] = E[N2 | N > 0]P{N...

Q:

*17. Let N be a nonnegative, integer-valued random variable. Show that and explain how this inequality can be used to derive additional bounds on a reliability function. Now multiply both sides by .

Q:

Two lives aged x and y take out a policy that will pay out 15,000 on the death of (x) provided that (y) has died at least 5 years earlier and no more than 15 years earlier. (1) Express the present...

Q:

The dot product can be used for determining the angle between two vectors: Use MATLAB's built-in functions acosd, sqrt, and dot to find the angle (in degrees) between r1 = 6i - 3j + 2k and r2 = 21 +...

Q:

A B describes a ) total variable cost, 1 0 0 units b ) number units sold at 1 0 0 $ profit c ) contribution mavgin at 1 0 0 units d ) amount of profit

Q:

What is the definition of cooperative strategy, and why is this strategy important to firms competing in the current competitive landscape?

Q:

10.8. Use the approximation of Section 10 3 to approximate P(system failure) in Problem

Q:

Also determine the bound provided by Corollary 10.3.2.

Q:

Suppose that W is the sum of independent Bernoulli random variables. Bound the difference between P{W =k} and its approximation as given in Equation (10.3.1). Compare this bound with the one obtained...

Q:

Check my work Return to question Problem 24-37 (LO 24-1) (Algo) Spartan Corporation, a U.S. corporation, reported $3.9 million of pretax income from its business operations in Spartania, which were...

Q:

Entries Record the following transactions as journal entries. Received $5,000 from selling shares of stock Date Nov. 3 Accounts and Explanation Purchase a $7,000 building with note Date Nov. 4 Debit...

Q:

Proust Company has FCFF of $ 1.9 billion and FCFE of $1.6 billion. Proust's WACC is 12 percent, and its required rate of return for equity is 15 percent. FCFF is expected to grow forever at 6.5...