## Probability and random process

Let V₁ and r be two independant random variables such that V₁ is normal N(m,σ²) and r is uniform in [0,1].

A random process is given by:
X(t)=V₁I(r<t)-V₁I(r≥t) where I(r≥t) and I(r<t) denote the indicator function

a)Find the expectation of this process: E(X(t)
I got E(X(t)=m-2mt

b)Find the autocorelation of this process R(t,s)=E[(X(t)X(s)]
for this bit i got: R(t,s)=σ²

I don't know if my answer is correct if someone could check if they get the same answer