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Exercise 1

Consider the simple linear regression model

\[ Y = -5 + 2.2x + \epsilon \]

where

\[ \epsilon \sim N(0, \sigma^2 = 16). \]

Calculate two probabilities using this model:

\[ P\left[Y > 8 \mid X = 2 \right] \]

\[ P\left[Y > 8 \mid X = 4 \right] \]


Exercise 2