Statistical Inference Question

  • Thread starter thebook
  • Start date
  • #1
1
0
Hi guys,

I am stuck with this problem... Please help!

Define the rounding function [.] to integers as follows:

[x] = j if x ∈ (j-0.5, j+0.5, for j = 0,+-1, +-2,...

Suppose X has a uniform distribution on the interval (a,b). i.e., X~U(a,b) a<b.

1. find a pair a and b such hat Var(X) > Var([X]) and such that VAR(X) < VAR([X])
2. Suppose that a random variable X has a continuous CDF F(x). What are the distributions of F(X) and [F(X)]? and finally R = [F(X)]-F(X)?
 

Answers and Replies

  • #2
Stephen Tashi
Science Advisor
7,389
1,367
1. find a pair a and b such hat Var(X) > Var([X]) and such that VAR(X) < VAR([X])
Instead of what you wrote, I think the question should say:

1. Find a pair of numbers (a,b) such that Var(X) > Var([X]) and find another pairs of numbers (a,b) such that Var(X) < Var([X]).
 
  • #3
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
34,551
5,966
2. Suppose that a random variable X has a continuous CDF F(x). What are the distributions of F(X) and [F(X)]? and finally R = [F(X)]-F(X)?
F(X) doesn't mean anything, and neither does 'the distribution of F(x)'. F(x) is the distribution of X.
Should it read:
What are the distributions of [X] and [X]-X?
 

Related Threads on Statistical Inference Question

  • Last Post
Replies
2
Views
2K
Replies
5
Views
2K
  • Last Post
Replies
1
Views
11K
  • Last Post
Replies
15
Views
4K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
8
Views
3K
  • Last Post
Replies
4
Views
4K
  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
0
Views
1K
Top