Solution
= Solution
{c}
A linear combination of independent <normal random variables> is normal. Its mean is $2\cdot0+0=0$, and independence removes the cross-covariance term in its variance:
$$
\boxed{X=2Z_1+Z_2\sim N(0,2^2+1^2)=N(0,5).}
$$
= Solution
{c}
A linear combination of independent <normal random variables> is normal. Its mean is $2\cdot0+0=0$, and independence removes the cross-covariance term in its variance:
$$
\boxed{X=2Z_1+Z_2\sim N(0,2^2+1^2)=N(0,5).}
$$