{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# hw4 - 36-226 Summer 2010 Homework 4 Due July 12 1 Assume...

This preview shows pages 1–2. Sign up to view the full content.

36-226 Summer 2010 Homework 4 Due July 12 1. Assume that X , the proportion of defective products that a machine produces in a day, has the following density: f X ( x | θ ) = θ (1 - x ) θ - 1 I (0 , 1) ( x ) . Note that this is a Beta(1, θ ) distribution. In order to estimate θ , the machine was observed for 100 days and the proportion of defective products was recorded for each day. The data is in the R file Defects.Rdata that is linked from the HW section of the course website. The name of the dataset is defects . It is a vector with 100 entries. (a) Find a method of moments estimator for θ based on a random sample of size n from the above distribution. (b) Find a maximum likelihood estimator for θ . (c) Use part (a) and the data to find an estimate for θ . (d) Use part (b) and the data to find a second estimate for θ . (e) Use your estimates from part (c) and (d) to estimate the probability that on a given day, the proportion of defective products will exceed .025 2. Let X 1 , X 2 , . . . , X n be a random sample from the following distribution: f X ( x | θ ) = 3 x 2 θ 3

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

hw4 - 36-226 Summer 2010 Homework 4 Due July 12 1 Assume...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online