This discussion is closed.
Badges: 0
Report Thread starter 14 years ago
Review exercise 1, Number 19:

A consumer group is investigating telephone usage within a particular city. The numbers of telephone units, x, used in a particular quarter by a random sample of 250 households were summarised in a group frequency table. In order to simplify the arithmetic the data in the table were coded such that :
y=x-290 / 10, giving (Sigma symbol)fy=-40 and (sigma symbol)fy^2=1075
a) Find estimates of the mean and the variance of the number of telephone units used in that quarter by households in the city.

How do I do this Question?
Jonny W
Badges: 8
Report 14 years ago
You need to know the following results. They are valid for any random variable X and any numbers a and b.

E(aX + b) = a E(X) + b
Var(aX + b) = a^2 Var(X)


Let X be the telephone usage of a randomly selected household in the city. Let Y be the coded telephone usage of that household.

Then Y = (X - 290)/10. So X = 10Y + 290.

E(X) = 10 E(Y) + 290
Var(X) = 10^2 Var(Y) = 100 Var(Y)

Estimate E(Y) and Var(Y) using the data. Then use the above formulas to estimate E(X) and Var(X).
new posts
to top
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.


University open days

  • Bournemouth University
    Midwifery Open Day at Portsmouth Campus Undergraduate
    Wed, 16 Oct '19
  • Teesside University
    All faculties open Undergraduate
    Wed, 16 Oct '19
  • University of the Arts London
    London College of Fashion – Cordwainers Footwear and Bags & Accessories Undergraduate
    Wed, 16 Oct '19

How has the start of this academic year been for you?

Loving it - gonna be a great year (110)
It's just nice to be back! (166)
Not great so far... (221)
I want to drop out! (117)

Watched Threads

View All