ZuoTi.Pro
Question

Let σ2 be the variance of a random variable X, show that σ2 = μ′2 −...

Let σ2 be the variance of a random variable X, show that σ2 = μ′2 − μ2 where μ′2 is the second moment about the origin and μ is the mean of X.
math   Statistics-And-Probability   
0 0
Add a comment Improve this question Transcribed image text
Next > < Previous
Sort answers by oldest

Homework Answers

Answer #1

FAGC Na. // CATE So1 etion Yaiabe Let oandom be 62 is voianse of and know hat Cwe oa moment obou original of andom variaple -PAGE No. DATE For conhn uous, Therefore ECR- CA-A)or dr -22 fCR d- fCR2a= fcr d 1 Now ECR-RIR) EIn-e)x) avelationshipbetcoeenPAGE NO, DATE Therefore = Hence pooof Now, for Onderstonding YOTCA=E(r2)-(EC) here ECD Theiefore, EC)-(Er)) Cs Sdanned with C

0 0
Add a comment
Know the answer?
Add Answer to:
Let σ2 be the variance of a random variable X, show that σ2 = μ′2 −...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions

  • Let X,,X.X be a random sample of size n from a random variable with mean and variance given by (μ, σ2) a Show that the...

    Let X,,X.X be a random sample of size n from a random variable with mean and variance given by (μ, σ2) a Show that the sample meanX is a consistent estimator of mean 1(X-X)2 converges in probability Show that the sample variance of ơ2-02- b. 1n to Ơ2 . Clearly state any theorems or results you may have used in this proof. Let X,,X.X be a random sample of size n from a random variable with mean and variance given...

  • Let X be a random variable with mean μ and variance σ2, and let Y be...

    Let X be a random variable with mean μ and variance σ2, and let Y be a random variable with mean θ and variance τ2, and assume X and Y are independent. (a) Determine an expression for Corr(X Y , Y − X ). (b) Under what conditions on the means and variances of X and Y will Corr(XY, Y −X) be positive (i.e., > 0 )?

  • Problem 5 of 5Sum of random variables Let Mr(μ, σ2) denote the Gaussian (or normal) pdf with Inea...

    Problem 5 of 5Sum of random variables Let Mr(μ, σ2) denote the Gaussian (or normal) pdf with Inean ,, and variance σ2, namely, fx (x) = exp ( 2-2 . Let X and Y be two i.i.d. random variables distributed as Gaussian with mean 0 and variance 1. Show that Z-XY is again a Gaussian random variable but with mean 0 and variance 2. Show your full proof with integrals. 2. From above, can you derive what will be the...

  • 4.48 A Gaussian random variable has mean μ and variance σ2 (a) Show that the moment geneng fnctio...

    Please solve this. Thank you. 4.48 A Gaussian random variable has mean μ and variance σ2 (a) Show that the moment geneng fnction (MGF) for the Gaussian ran dom variable is given by Hint: Use the technique of "completing the square. b) Assume that 0 and use the MGF to compute the first four moments of x a well hvarian, sks, and kurtosis. (c) What are the mean, variance, skewness, and kurtosis for μ 0? 4.48 A Gaussian random variable...

  • Let X = (X1, . . . , Xn) be a random sample of size n with mean μ and variance σ2. Consider Tm i=...

    Let X = (X1, . . . , Xn) be a random sample of size n with mean μ and variance σ2. Consider Tm i=1 (a) Find the bias of μη(X) for μ. Also find the bias of S2 and ỡXX) for σ2. (b) Show that Hm(X) is consistent. (c) Suppose EIXI < oo. Show that S2 and ỡXX) are consistent. Let X = (X1, . . . , Xn) be a random sample of size n with mean μ...

  • Let X be a random variable with cdf FX (x:0), expected value EIX-μ and variance VlX- σ2. Let X1,X...

    Let X be a random variable with cdf FX (x:0), expected value EIX-μ and variance VlX- σ2. Let X1,X2, , Xn be an id sample drawn according to FX(x,8) where Fx (x,8) =万 for all x E (0,0). Let max(X1, X2, , X.) be an estimator of θ, suggested from pure common sense. Remember that if Y = max(X1, X2, , Xn). Then it can be shown that the cdf Fy () of Y is given by Fr(u) (Fx()" where...

  • 5) Let X be a random variable with mean E(X) = μ < oo and variance...

    5) Let X be a random variable with mean E(X) = μ < oo and variance Var(X) = σ2メ0. For any c> 0, This is a famous result known as Chebyshev's inequality. Suppose that Y,%, x, ar: i.id, iandool wousblsxs writia expliiniacy" iacai 's(%) fh o() airl íinic vaikuitx: Var(X) = σ2メ0. With Υ = n Ση1 Y. show that for any c > 0 Tsisis the celebraed Weak Law of Large Numben

  • Problem 2. Let X be a random variable with mean 0 and variance σ2. Define the...

    Problem 2. Let X be a random variable with mean 0 and variance σ2. Define the process Yt-(-1) Compute the mean and covariance function of the process {Yt). Is this process stationary?

  • 1 Let X be a discrete random variable. (a) Show that if X has a finite...

    1 Let X be a discrete random variable. (a) Show that if X has a finite mean μ. then EX-ix-0. (b) Show that if X has a finite variance, then its mean is necessarily finite 2 Let X and Y be random variables with finite mean. Show that, if X and Y are independent, then 3 Let Y have mean μ and finite variance σ2 (a) Use calculus to show that μ is the best predictor of Y under quadratic...

  • Let X and Y be two independent Gaussian random variables with common variance σ2. The mean of X i...

    Let X and Y be two independent Gaussian random variables with common variance σ2. The mean of X is m and Y is a zero-mean random variable. We define random variable V as V- VX2 +Y2. Show that: 0 <0 Where er cos "du is called the modified Bessel function of the first kind and zero order. The distribution of V is known as the Ricean distribution. Show that, in the special case of m 0, the Ricean distribution simplifies...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT