- #1
nickthegreek
- 12
- 0
Homework Statement
We have an interval [0,1], which we divide into k equally sized subintervals and generate n observations. Let's call the number of observations which falls into interval k_i, X_i. What distribution does X_1 have?
Now we define Y_i=X_i/n. Derive the Expected value, variance and standard deviation for Y_i?
This is a homework assignment, so please just guide me... don't give me the answers :)
Homework Equations
The Attempt at a Solution
The distribution for X_1: The amount of observations in each interval should follow a normal distribution, no? But the number of observations in each interval will be discrete? If I could understand what distr. this is, I could solve for E(X_i^2) in the last expression?
X_i=# of n that is in k_i. So, E(X_i)=n/k.
E(Y_i)=E(X_i/n)=(1/n)(E(X_i))=1/k
V(Y_i)=E((Y_i)^2)-(E(Y_i))^2=E((X_i/n)^2)-(1/k)^2=(1/n)^2*E(X_i^2)-1/k^2 ?