Conditional distribution of iid variables

Question

I am given several four iid random variables (say a, b, c, d), each with a distribution of N(0.2,0.01). How does the sum of these four iid RVs (i.e. Z=a+b+c+d) distribute under the condition of d=0.3? I thought this should be the same as Z's distribution without the condition since a~d are iid.

Answer 1

The conditional distribution is the same as that of $a+b+c+0.3$.

So it is normal, mean $(3)(0.2)+0.3$.

I do not know whether your $0.01$ refers to variance or standard deviation. Using variance as the parameter is more usual, but in elementary courses sometimes standard deviation is used as the parameter.

If it is variance, our random variable has variance $(3)(0.01)$. If it is standard deviation, then your random variable has standard deviation $(\sqrt{3})(0.01)$.