(d) (2 points) Fix a sample size no = [51:32:]. For each of the group means i, we dene a binary random variable Zi: Zz' = 103\") Ml Z 6)- In other words, Z- is 1 if the correSponding group mean is close to the true mean it (within 6), and 0 otherwise. Show that IE[ZZ] g 1/4. Hint: Zi is a Bernoulli random variable. (e) (2 points) We set SMed := Median({8(1),...,8(m)}). This is called the medianof means estimator. Explain in words Why having |SMed ,a| 2 6 implies that 22:1 ZZ- 2 m 2 . Hint: If y is the median of m numbers, it means that I'm/2] of the numbers are greater than or equal to y, and similarly [in/2] of the numbers are less than or equal to y