Question

We have a value Y dependent on a set of independent random variables X1, X2,..., Xn...

We have a value Y dependent on a set of independent random variables X1, X2,..., Xn by the following relation: Y=X12+X22+...+Xn2. Each of X variables is distributed via the normal distribution with following parameters:

1. Mean values of all Xi = 0

2. Variances are identical and are equal to ak2

Find probability density of a random value of Y.

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

Homework Answers

Answer #1

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,X2,..., Xn be independent random variables that are exponentially distributed with respective parameters λ1,λ2,..., λn....
Let X1,X2,..., Xn be independent random variables that are exponentially distributed with respective parameters λ1,λ2,..., λn. Identify the distribution of the minimum V = min{X1,X2,...,Xn}.
Let X1, X2,... be a sequence of independent random variables distributed exponentially with mean 1. Suppose...
Let X1, X2,... be a sequence of independent random variables distributed exponentially with mean 1. Suppose that N is a random variable, independent of the Xi-s, that has a Poisson distribution with mean λ > 0. What is the expected value of X1 + X2 +···+ XN2? (A) N2 (B) λ + λ2 (C) λ2 (D) 1/λ2
Suppose that X1, X2, . . . , Xn are independent identically distributed random variables with...
Suppose that X1, X2, . . . , Xn are independent identically distributed random variables with variance σ2. Let Y1 = X2 +X3 , Y2 = X1 +X3 and Y3 = X1 + X2. Find the following : (in terms of σ2) (a) Var(Y1) (b) cov(Y1 , Y2 ) (c) cov(X1 , Y1 ) (d) Var[(Y1 + Y2 + Y3)/2]
Consider n independent variables, {X1, X2, . . . , Xn} uniformly distributed over the unit...
Consider n independent variables, {X1, X2, . . . , Xn} uniformly distributed over the unit interval, (0, 1). Introduce two new random variables, M = max (X1, X2, . . . , Xn) and N = min (X1, X2, . . . , Xn). (A) Find the joint distribution of a pair (M, N). (B) Derive the CDF and density for M. (C) Derive the CDF and density for N. (D) Find moments of first and second order for...
Continuous random variables X1 and X2 with joint density fX,Y(x,y) are independent and identically distributed with...
Continuous random variables X1 and X2 with joint density fX,Y(x,y) are independent and identically distributed with expected value μ. Prove that E[X1+X2] = E[X1] +E[X2].
Suppose {x1,x2,...xn} is linear dependent and {x1,x2} is linear independent. Show that:  2 < than or equal...
Suppose {x1,x2,...xn} is linear dependent and {x1,x2} is linear independent. Show that:  2 < than or equal to (Span(x1,x2,...xn)) < n.
Let X1, X2, X3 be independent random variables, uniformly distributed on [0,1]. Let Y be the...
Let X1, X2, X3 be independent random variables, uniformly distributed on [0,1]. Let Y be the median of X1, X2, X3 (that is the middle of the three values). Find the conditional CDF of X1, given the event Y = 1/2. Under this conditional distribution, is X1 continuous? Discrete?
7.5) If X1 and X2 are independent random variables having exponential densities with the parameters θ1...
7.5) If X1 and X2 are independent random variables having exponential densities with the parameters θ1 and θ2, use the distribution function technique to find the probability density of Y=X1+X2 when a) θ1 ≠ θ2 b) θ1 = θ2 7.7) With reference to the two random variables of Exercise 7.5, show that if θ1 = θ2 = 1, the random variable Z1=X1/(X1 + X2) has the uniform density with α=0 and β=1.                                      (I ONLY NEED TO ANSWER 7.7)
7.5) If X1 and X2 are independent random variables having exponential densities with the parameters θ1...
7.5) If X1 and X2 are independent random variables having exponential densities with the parameters θ1 and θ2, use the distribution function technique to find the probability density of Y=X1+X2 when a) θ1 ≠ θ2 b) θ1 = θ2 7.7) With reference to the two random variables of Exercise 7.5, show that if θ1 = θ2 = 1, the random variable Z1=X1/(X1 + X2) has the uniform density with α=0 and β=1.                                      (I ONLY NEED TO ANSWER 7.7)
5. Let X1, X2, . . . be independent random variables all with mean E(Xi) =...
5. Let X1, X2, . . . be independent random variables all with mean E(Xi) = 7 and variance Var(Xi) = 9. Set Yn = X1 + X2 + · · · + Xn n (n = 1, 2, 3, . . .) (a) Find E(Y2) and E(Y5). (b) Find Cov(Y2, Y5). (c) Find E (Y2 | X1). (d) How should your answers from parts (a)–(c) be modified if the numbers “2”, “5”, “7” and “9” are replaced by m,...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT