Question

Let X1, X2, X3, and X4 be mutually independent random variables from the same distribution. Let...

Let X1, X2, X3, and X4 be mutually independent random variables from the same distribution. Let
S = X1 + X2 + X3 + X4. Suppose we know that S is a Chi-Square random variable with 2 degrees of freedom. What
is the distribution of each of the Xi?

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

Homework Answers

Answer #2

answered by: anonymous
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
Suppose X1, X2, X3, and X4 are independent and identically distributed random variables with mean 10...
Suppose X1, X2, X3, and X4 are independent and identically distributed random variables with mean 10 and variance 16. in addition, Suppose that Y1, Y2, Y3, Y4, and Y5are independent and identically distributed random variables with mean 15 and variance 25. Suppose further that X1, X2, X3, and X4 and Y1, Y2, Y3, Y4, and Y5are independent. Find Cov[bar{X} + bar{Y} + 10, 2bar{X} - bar{Y}], where bar{X} is the sample mean of X1, X2, X3, and X4 and bar{Y}...
1)Let X1, ..., Xn be independent standard normal random variables, we know that X2 1 +...
1)Let X1, ..., Xn be independent standard normal random variables, we know that X2 1 + ... + X2 n follows the chi-squared distribution of n degrees of freedom. Find the third moment of the the chi-squared distribution of 2 degrees of freedom. 2) Suppose that, on average, 1 person in 1000 makes a numerical error in preparing his or her income tax return. If 10,000 returns are selected at random and examined, find the probability that 6 or 7...
Let x1, x2 x3 ....be a sequence of independent and identically distributed random variables, each having...
Let x1, x2 x3 ....be a sequence of independent and identically distributed random variables, each having finite mean E[xi] and variance Var（xi）. a）calculate the var （x1+x2） b）calculate the var（E[xi]） c） if n-> infinite, what is Var（E[xi]）？
Let X1 , X2 , X3 , X4 be a random sample of size 4 from...
Let X1 , X2 , X3 , X4 be a random sample of size 4 from a geometric distribution with p = 1/3. A) Find the mgf of Y = X1 + X2 + X3 + X4. B) How is Y distributed?
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?
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 x1, x2, x3, x4 is linearly independent in V . Prove that x1 − x2,...
Suppose x1, x2, x3, x4 is linearly independent in V . Prove that x1 − x2, x2 − x3, x3 − x4, x4 is also linearly independent in V
Suppose that X1,X2 and X3 are independent random variables with common mean E(Xi) = μ and...
Suppose that X1,X2 and X3 are independent random variables with common mean E(Xi) = μ and variance Var(Xi) = σ2. Let V= X2−X3 and W = X1− 2X2 + X3. (a) Find E(V) and E(W). (b) Find Var(V) and Var(W). (c) Find Cov(V,W). (d) Find the correlation coefficient ρ(V,W). Are V and W independent?
Let X1, X2, X3, and X4 be a random sample of observations from a population with...
Let X1, X2, X3, and X4 be a random sample of observations from a population with mean μ and variance σ2. Consider the following estimator of μ: 1 = 0.15 X1 + 0.35 X2 + 0.20 X3 + 0.30 X4. Is this a biased estimator for the mean? What is the variance of the estimator? Can you find a more efficient estimator?) ( 10 Marks)
Let X1, X2, X3 be a random sample from a population. The distribution of the population...
Let X1, X2, X3 be a random sample from a population. The distribution of the population has a parameter θ, and it is known that E[Xi] = 2θ and Var[Xi] = σ2 for i = 1,2,3. Consider the following two point estimators for θ: W1= (1/8)X1+ (1/4)X2+ (1/8)X3 and W2= (1/6)X1+ (1/4)X2+ (1/12)X3 Which is the better estimator for θ? Why?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT