Gujarati-Example 4.03

[PDEM200]

Hi David,
Hoping you can clarify some aspects about problem 4.03 that were posted:

4.03d) In the calculation, why was a variance of 15 used and not 16 (as given in the problem)?

4.03e) Notation: How do you distinguish a normal distribution from a "standard" normal distribution? Does "N" always signal Standard Normal Distribution?

Thank you

 

[David Harper CFA FRM]

Hi Paul,

04.03d: My mistake, sorry. As you suggest, Standard Error = SQRT(16/25). The 0.98% answer reflects the correct '16' rather than the incorrect '15'

04.03e. N() connotes normal as in ~N(mean, variance) so the standard normal is written as N(0,1). (Gujarati p 80). I didn't mean to be cute, just years ago there was a question "how many params does a standard normal have?" and technically it is 0 b/c standard implies mean=0, variance = 1. (Although I hate this question, b/c i feel you could argue the standard normal has two params)

some people in my understanding use Z to connote standard normal. So, you see Z ~ N(0,1).
e.g., the normal lookup tables in back of the stat table are called, after all, critical z values and those, by definition are "standard normals"
but I *think* the Z refers to the standarized not the normal part, just as we can standardize the t. So I am not sure the 'Z' technically implies standard normal, or i think it just implies standardized. So, I think Z is used to connote standard normal, but i am unsure about the correctness of this. Regardless, N(0,1) is very clear.

David