Question: Let [ Z I , II ) . .... I Z'n , I'd be generated as follows : { ~` Bernoulli(p ) IN 10, 1

Let [ Z I , II ) . .... I Z'n , I'd be generated as follows :" { ~` Bernoulli(p ) IN 10, 1 ) if Z = 1) if 2 = 1. [a] ASSUME WE do not observe the Z's. Write the pdf fluj of'{" as a mixture of two normal distribution put . ( Use the notation {! . I which is the standard normal pdf . ! I bj Write down the likelihood function for " ( without { 's )` Icj Write down the complete likelihood function for ! ( assuming the {'s are observed ) . I'd! Find the maximum likelihood estimation of ! using the likelihood from ( c )

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