MATLAB Random Number Generator

Question

I'm a beginner in Matlab and I can't solve the problem below.

"Starting with z (0,1) Gaussian Random variable; generate 10000 random variables with mean 10, variance 1; call it r6 vector.

At first glance, I tried to write r6=10+1*randn(10000,1); but I am not sure whether it's correct or not. Any help will be appreciated. Many thanks

• Pursuit: That's right. Looks like you have this nailed.
• Luis Mendo: I'd only add a sqrt: r6=10+sqrt(1)*randn(10000,1);. Of course with 1it makes no difference; I mean the general case
• Buck Thorn: @LuisMendo Good point, overlooked that and the OP maybe too!
• Luis Mendo: No. r6=10+1*rand(10000,1) would give you a uniform RV (not Gaussian) with std equal to 1/sqrt(12) (not 1)
• Luis Mendo: Why: just compute the variance of a pdf which is 1 in [0 1] and 0 outside that interval. Or see here. To generate uniform random numbers with mean 10 and variance 1: r6=10+sqrt(12)*(rand(10000,1)-.5). I'll let you figure out why this is so :-)

Answer 1

You can test whether you have the right mean and std deviation of your distribution after the fact with

 mean(r6)
 std(r6)

Note that as LuisMendo rightly points out you were issued the variance so you should make sure to take roots/square stuff as appropriate:

 variance = std(r6)^2

• Luis Mendo: @Jason Also note that mean(r6) and std(r6) are the sample mean / standard deviation, which are only approximations to the "true" mean / standard deviation. So you should expect some deviations in the obtained values; those deviations will of course diminish with the size of r6.