Question: (a) Consider a random variable uniformly distributed between 0 and 2. Show that E(X 2 ) > E 2 (X). (b) Consider a random variable

(a) Consider a random variable uniformly distributed between 0 and 2. Show that E(X2) > E2(X).

(b) Consider a random variable uniformly distributed between 0 and 4. Show that E(X2) > E2(X).

(c) Can you show in general that for any random variable it is true that E(X2) > E2(X) unless the random variable is zero almost always?

(Expand E {[X - E(X)]2 ≥ 0} and note that it is 0 only if X = 0 with probability 1.)

Step by Step Solution

★★★★★

3.46 Rating (172 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a So it is true in this special case b So it is ... View full answer

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 Principles Communications Systems Questions!

Q:

Consider a random process X (t) defined by X (t) = sin (2fct), in which the frequency f c is a random variable uniformly distributed over the interval [0, W]. Show that X (t) is non-stationary

Q:

Two random processes are given by X (t) = n (t) + A cos(2f 0 t + ) and Y (t) = n (t) + A sin(2f 0 t + ) Where A and f 0 are constants and is a random variable uniformly distributed in the interval...

Q:

Consider two conducting spheres with radii R1 and R2. They are separated by a distance much greater than either radius. A total charge Q is shared between the spheres, subject to the condition that...

Q:

An analyst has available two forecasts, F1 and F2, of earnings per share of a corporation next year. He intends to form a compromise forecast as a weighted average of the two individual forecasts. In...

Q:

I need help with this question please 2.2. Get a random number generator for n = min (1,32,83) wheree 1, E2, E3 are independent random variables with exponential distribution: prob( > x) = prob (2,>...

Q:

Problem 5 Let X be a random variable, uniformly distributed on (0, 1), and let Y be a random variable uniformly distributed on (0, 2). With X and Y indepen dent. 1. Find the probability density of X...

Q:

Problem 5 Let X be a random variable, uniformly distributed on (0, 1), and let Y be a random variable uniformly distributed on (0, 2). With X and Y indepen dent. 1. Find the probability density of X...

Q:

only do coding using Jupyter (python programming) ignore the writing Writing and Coding) Suppose X, are i.i.d. random variable uniformly distributed in [0, 1]. Let Sn X, be the sum of n random...

Q:

Airlines in the United Statesuse a practice called "overbooking" (or oversales) in which an airline sells more tickets for a flight than there are seats on the airplane. In that case, it's possible...

Q:

in R Write a script that, for the numbers 1 through 100, will print YAY if the number is divisible by 3, BOO if it is divisible by 5, YAYBOO if it divisible by 3 and 5. For any odd number that does...

Q:

Apr. 15. Received $800 from Jean Tooley and wrote off the remainder owed of $1,200 as uncollectible. Aug. 7. Reinstated the account of Jean Tooley and received $1,200 cash in full payment. Journalize...

Q:

Suppose that an estimate of U.S. federal spending showed that 46% was for entitlements, 18% was for defense, 15% was for grants to states and localities, 14% was for interest on debt, 6% was for...

Q:

9. Suppose the marginal benefit of writing a contract is $100, independent of its length. Find the optimal contract length when the marginal cost of writing a contract of length L is: (LO3) a. MC(L)...

Q:

A business firm produces a good this year that it doesnt sell. As a result, the good is added to the firms inventory. How does this inventory good find its way into GDP?

Q:

A speed skater moving to the left across friction less ice at 8.0 m/s hits a 5.0-m-wide patch of rough ice. She slows steadily, then continues on at 6.0 m/s. What is her acceleration on the rough ice?

Q:

A Porsche challenges a Honda to a 400 m race. Because the Porsches acceleration of 3.5 m/s 2 is larger than the Hondas 3.0 m/s 2 , the Honda gets a 1.0 s head start. Who wins? By how many seconds?

Q:

A car starts from rest at a stop sign. It accelerates at 4.0 m/s 2 for 6.0 s, coasts for 2.0 s, and then slows down at a rate of 3.0 m/s 2 for the next stop sign. How far apart are the stop signs?

Q:

The owner of an antique store estimates that there is a 35% chance she will make $2400 when she sells an antique chinacabinet, a 60% chance she will make $900 when she sells thecabinet, and a 5%...

Q:

1 . What would be the impact on the company s financial statement if PolyMedica had expensed the costs as incurred in 2 0 0 3 and 2 0 0 2 ? Calculate key balances that highlight any major differences...

Q:

ACTUARIAL solution please A stock pays annual dividends at the end of each year. The earnings per share in the year just ended were $102. Earnings are assumed to grow at 7.3% per year in the future....