Question

Problem 1.10: Let P1 and P2 be two probability functions on Ω. Defne a new function...

Problem 1.10: Let P1 and P2 be two probability functions on Ω. Defne a new function P such that P(A) = (P1(A) + P2(A))/2. Show that P is a probability function.

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

Homework Answers

Answer #1

Given, P1 and P2 are two probability functions on .

Then, for any set A on ,

  & and

&

Define , function such that

Then,

&

and

Hence, is a probability function. Proved

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 the indirect utility functions is: v(p1, p2, m) = ( ln(m /p2) , if p1...
Suppose the indirect utility functions is: v(p1, p2, m) = ( ln(m /p2) , if p1 ≥ m. (m−p1)/ p1 + ln(p1/ p2 ), if p1 < m. a) Compute the Marshallian demand for both goods x1 and x2 for the different values of m. b) Based on your answers from (a), can you guess the type of the original utility function u(x) (Hint: It is one of the 5 common utility functions we have taken in the course)? Explain...
Suppose the indirect utility functions is: v(p1, p2, m) = ln (m /p2) , if p1...
Suppose the indirect utility functions is: v(p1, p2, m) = ln (m /p2) , if p1 ≥ m.( m−p1)/ p1 + ln (p1/ p2) , if p1 < m. a) Compute the Marshallian demand for both goods x1 and x2 for the different values of m. b) Based on your answers from (a), can you guess the type of the original utility function u(x) (Hint: It is one of the 5 common utility functions we have taken in the course)?...
In this question we denote by P2(R) the set of functions {ax2 + bx + c...
In this question we denote by P2(R) the set of functions {ax2 + bx + c : a, b, c ∈ R}, which is a vector space under the usual addition and scalar multiplication of functions. Let p1, p2, p3 ∈ P2(R) be given by p1(x) = 1, p2(x) = x + 2x 2 , and p3(x) = αx + 4x 2 . a) Find the condition on α ∈ R that ensures that {p1, p2, p3} is a basis...
Let p1,p2 denote the probability that a randomly selected male and female, respectively, has allergy to...
Let p1,p2 denote the probability that a randomly selected male and female, respectively, has allergy to nuts. Let n1,n2 be the sample size of a random sample for male and female, respectively. Assume two samples are indepedent. Let X1,X2 be the number of male and female who have allergy to nuts in the random sample, respectively. (1)(3pts) For parameters p1,p2, and p1−p2, find one unbiased estimator for each of them. And show why they are unbiased. (2)(3pts) Derive the formula...
Let p1,p2p1,p2 denote the probability that a randomly selected male and female, respectively, has allergy to...
Let p1,p2p1,p2 denote the probability that a randomly selected male and female, respectively, has allergy to nuts. Let n1,n2n1,n2 be the sample size of a random sample for male and female, respectively. Assume two samples are indepedent. Let X1,X2 be the number of male and female who have allergy to nuts in the random sample, respectively. (1)(3pts) For parameters p1,p2,p1,p2, and p1−p2p1−p2, find one unbiased estimator for each of them. And show why they are unbiased. (2)(3pts) Derive the formula...
Let P be a probability distribution on sample space Ω and A ⊂ Ω an event...
Let P be a probability distribution on sample space Ω and A ⊂ Ω an event such that P(A) > 0. Show that the conditional probability given A is a proper probability distribution on Ω using the axioms of probability and definition of conditional probability.
Find the expenditure function, the Hicksian demand functions, and the Marshallian demand functions corresponding to the...
Find the expenditure function, the Hicksian demand functions, and the Marshallian demand functions corresponding to the indirect utility function V(p, r) = (a1/p1 + a2/p2)r. Note p is a vector of prices p1 and p2.
2. Let P 1 and P2 be planes with general equations P1 : −2x + y...
2. Let P 1 and P2 be planes with general equations P1 : −2x + y − 4z = 2, P2 : x + 2y = 7. (a) Let P3 be a plane which is orthogonal to both P1 and P2. If such a plane P3 exists, give a possible general equation for it. Otherwise, explain why it is not possible to find such a plane. (b) Let ` be a line which is orthogonal to both P1 and P2....
1. Consider this hypothesis test: H0: p1 - p2 = 0 Ha: p1 - p2 >...
1. Consider this hypothesis test: H0: p1 - p2 = 0 Ha: p1 - p2 > 0 Here p1 is the population proportion of “yes” of Population 1 and p2 is the population proportion of “yes” of Population 2. Use the statistics data from a simple random sample of each of the two populations to complete the following: (8 points) Population 1 Population 2 Sample Size (n) 400 600 Number of “yes” 300 426 Compute the test statistic z. What...
Two firms compete by choosing price. Their demand functions are Q1 = 20 - P1 +...
Two firms compete by choosing price. Their demand functions are Q1 = 20 - P1 + P2 and Q2 = 20 +P1 -P2 where P1 and P2 are the prices charged by each firm, respectively, and Q1 and Q2 are the resulting demands. Note that the demand for each good depends only on the difference in prices; if the two firms colluded and set the same price, they could make that price as high as they wanted, and earn infinite...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT