Turn on thread page Beta

Probability - cumulative distribution and bias watch

    • Thread Starter
    Offline

    0
    ReputationRep:
    I have 2 questions that I'm stuck on.

    1)
    The cumulative distribution function for X is

    0, if x is less than or = 0
    x, if x is between 0 and 1
    1, if x is greater than or = 0

    Then find the cumulative distribution function of the random variable Y = -2lnX

    Find the probability density function of Y and identify the distribution.
    Also determine variance of Y.

    2)
    Suppose that X1, X2,... ,Xn is a random sample of size n, from a normal distribution N(0,theta).

    State whether the following are biased or unbiased, justify this.
    If they are biased, calculate the bias.

    theta hat = sigma(from i=1 to n) (((Xi)^2)/n)

    theta2 hat = n*[sigma(from i=1 to n) (Xi/n)^2 ]^2

    Thanks for any help!
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: December 3, 2011

University open days

  • University of East Anglia (UEA)
    Could you inspire the next generation? Find out more about becoming a Secondary teacher with UEA… Postgraduate
    Thu, 18 Oct '18
  • University of Warwick
    Undergraduate Open Days Undergraduate
    Sat, 20 Oct '18
  • University of Sheffield
    Undergraduate Open Days Undergraduate
    Sat, 20 Oct '18
Poll
Who is most responsible for your success at university
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Equations

Best calculators for A level Maths

Tips on which model to get

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.