Question

Really short question! Please help me to solve, thank you! Yet, the data set is too big (n=8000) as I can’t show all of them. Hope that the information of the second picture would be helpful.

(30%)Q4 (EM algorithm): The heights of n 8000 students are drawn from a school. Assume the height largely depends on the gender. We denote the height of student i by Yi, and the gender of student i by Z..(Y; : 1 i n) are observed, but {Zi : 1 i n} are unknown Our model can be formulated as follows. First, Pr(Zi 1) π and Pr(Z-2)-1-T, where Zi indicates student i is female. Zi--2 indicates student i is male, and π can be interpreted as the proportion of female students in all the students. Second, given Z, 1, Y, is assumed to be from a normal distribution N(μί, σ?); given Zi 2, X is assumed to be from, a normal distribution N(Paơ). Based on these notations and information, please 1) write down the cornplete-data likelihood function L(π, μί, μ2.σί, σ2/Y, Z); 2) derive E step and M step to find MLE of (π, μ, μ2: σί, σ2); 3) use R to implement your EM algorithm, give MLE of (π, μ, μ2:qM), and distinguish the first ten students' gender. (The data set (Y: 1Si S n) is "heights.data.tat".)

Answer 1

Answer:

By using given data ,the coding as follows bellow,

output: