Question

If X1, X2 are random sample from a distribution which is N(0,1), find the joint p.d.f...

If X1, X2 are random sample from a distribution which is N(0,1), find the joint p.d.f of Y1 = (X1)^2 + (X2)^2 and the marginal p.d.f of Y1

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Let X1 and X2 be two independent random samples from standard normal populations.

then distribution.

[If you need the derivation, let me know below.]

Where pdf of Y1 is given by :

this is the distributio of exp(2) also.

Do you mean conditional distribution in the 2nd part of the problem? or marginal distribution of X1 and X2? because marginal distribution of Y1 does not make any sense.

Let me know in the comment section, I will complete it as soon as you tell me.

This is the general case. Your question was for n = 2 .

*NB: X1,X2 must be independent of each other, else this would not be valid.

0 0
Know the answer?
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
Similar Questions
Let X1 and X2 be independent random variables with joint pdf f(x1, x2) =x1e^−(x1+x2), 0< x1<∞,...
Let X1 and X2 be independent random variables with joint pdf f(x1, x2) =x1e^−(x1+x2), 0< x1<∞, 0< x2<∞. Y1= 2X1 and Y2=X2−X1. I) Find g(y1, y2), the joint pdf of Y1, Y2 Include and draw the support. II) Find g1(y1), the marginal pdf of Y1. III) Find E(Y1).
(i) Find the marginal probability distributions for the random variables X1 and X2 with joint pdf...
(i) Find the marginal probability distributions for the random variables X1 and X2 with joint pdf                     f(x1, x2) = 12x1x2(1-x2) , 0 < x1 <1   0 < x2 < 1 , otherwise             (ii) Calculate E(X1) and E(X2)     (iii) Are the variables X1 ­and X2 stochastically independent? Given the variables in question 1, find the conditional p.d.f. of X1 given 0<x2< ½ and the conditional expectation E[X1|0<x2< ½ ].
Let X1, X2 be a random sample of size 2 from the standard normal distribution N...
Let X1, X2 be a random sample of size 2 from the standard normal distribution N (0, 1). find the distribution of {min(X1, X2)}^2
5. Let a random sample, X1, X2, ..., Xn of size n = 10 from a...
5. Let a random sample, X1, X2, ..., Xn of size n = 10 from a distribution that is N(μ1, σ2 ) give ̄x = 4.8 and s 2+ 1 = 8.64 and a random sample, Y1, Y2, ..., Yn of size n = 10 from a distribution that is N(μ2, σ2 ) give y ̄ = 5.6 and s 2 2 = 7.88. Find a 95% confidence interval for μ1 − μ2.
Q: Would like to clearly understand and solve this example from Probability and Statistical Inference with...
Q: Would like to clearly understand and solve this example from Probability and Statistical Inference with the steps of the solution to better understand, thanks. **Please explain and give the step by step with details to completely see how the solution came about, plenty of thanks. 1) a) Let X1, X2 denote two independent random variables, each with a χ2 (3) distribution. Find the joint p.d.f. of Y1=X1 and Y2=X2+X1. Here note that the support of Y1, Y2 is 0...
Let X1 and X2 be a sample from a uniform distribution on [0, 1] and let...
Let X1 and X2 be a sample from a uniform distribution on [0, 1] and let Y1 = min{X1, X2}, Y2 = max{X1, X2}. Find fY1 (y1|Y2 = y2). A. 1/ 2 B. 1 / 2y2 C. 1 /y2 D. 2 E. 1
Let X1, X2, · · · , Xn be a random sample from the distribution, f(x;...
Let X1, X2, · · · , Xn be a random sample from the distribution, f(x; θ) = (θ + 1)x^ −θ−2 , x > 1, θ > 0. Find the maximum likelihood estimator of θ based on a random sample of size n above
Let X1, X2, . . . , Xn be a random sample of size n from...
Let X1, X2, . . . , Xn be a random sample of size n from a distribution with variance σ^2. Let S^2 be the sample variance. Show that E(S^2)=σ^2.
(i) Find the marginal probability distributions for the random variables X1 and X2 with joint pdf...
(i) Find the marginal probability distributions for the random variables X1 and X2 with joint pdf f(x1, x2) = 12x1x2(1-x2) , 0 < x1 <1 0 < x2 < 1 0 , otherwise (ii) Calculate E(X1) and E(X2) (iii) Are the variables X1 ¬and X2 stochastically independent?
4. (i) Find the marginal probability distributions for the random variables X1 and X2 with joint...
4. (i) Find the marginal probability distributions for the random variables X1 and X2 with joint pdf                     f(x1, x2) = 12x1x2(1-x2) , 0 < x1 <1   0 < x2 < 1 , otherwise             (ii) Calculate E(X1) and E(X2)     (iii) Are the variables X1 ­and X2 stochastically independent?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT