two sample normal distribution

x_1,x_2,...,x_{n ~iid N (} mu_1, sigma₁²₎

_y1,y_2,...,y_{m~iid N (} mu_2, sigma₂²₎

_{would you write the joint pdf , then rewrite it as exponential family (as acanonical form), please}

i want the sufficient statistics to be ( x bar, y bar, S_x², S_y^2).