Generating random numbers with mean and std dev specified

Hi

I have a simple linear regression model y=10+25x+Ɛ where the random error term is normally and independently distributed with mean zero and standard deviation 2.

I have to generate 8 of these E values.

If I were to generate 5 random numbers between 4 an 7 (for example), then I'd usually use this: - x=4+(7-4)*rand(1,5); (i.e.,) vector=min+(max-min)*rand(r,c)

With this in mind, I was using the following, but the values aren't between -2 and 2:

E=-2+(2+2)*randn(1,8)

Can anybody point me in the right direction?

Thanks

Answer 1

[dpb]

The statistics for a normal are the mean and standard deviation, not the range of the observations as for a uniform, say. In fact, the standard normal variate is over range [-inf inf].

You state the desired error term is N(0,2) so the realization would be E = MEAN + STDev*randn(m,n), or in your specific case

E=2*randn(1,8);

since desired MEAN=0;

Your code above generates an approximation to N(-2,4) instead of N(0,2)

[Lorraine Williams]

Thank you. When I run E=2*randn(1,8), am I supposed to get random numbers between -2 and +2?

[Star Strider]

No. There is a 68% probability that they will be on the interval (-2,+2). They could theoretically be ±Inf.