15.1.15 Theory of random processes

Problem: Find the expected value, correlation function and the variance of the random function \( X(t)=X_{1} \cdot e^{2 t}-X_{2} \cdot \cos 5 t+3 t^{2}-1 \), where \( X_{1} \) and \( X_{2} \) are uncorrelated random variables with characteristics: \( m_{X_{1}}=0,2, m_{X_{2}}=0,3, D_{X_{1}}=0,01 \), \( D_{X_{1}}=0,04 \).