1.

\(p_0=0.5,\ \mu_1 = 10,\ \sigma_1=4,\ \mu_2=50,\ \sigma_2=10\)

\(p=\pi_1=0.333,\ \mu_1=9.965,\ \sigma_1=2.826,\ \mu_2 = 50.994\, \sigma_2=6.612\)

\(\sum p_i =1,\ \sum x_ip_i = \theta\)