Problem 1 Let X be a random normal variable with mean 4x (denoted by u = Ux) and standard deviation 0x (denoted by o = Ox), or formally: X~N(u = Mx, 0 = 0x) Let Y be a random normal variable with mean My (denoted by u = uy) and standard deviation Oy (denoted by o = Oy), or formally: Y-Nu = Hy, o = Oy) If Z = X + Y, then write R code to prove numerically that: Z follows a normal distribution with mean u = Mx + My and standard deviation or Voz +03; or formally, Z~N(u = Mx + My, 0 = 10 +03)