7. Consider the simple linear regression modelYᵢ = β₀ + β₁Xᵢ + εᵢ, Vᵢ = 1,2,...,n, and εᵢ's are i.i.d. N(0, σ²),Show that the least squares estimators of parameters β₀ and β₁ satisfyb₁ = ， andb₀ = whereare the sample means of the Xᵢ and Yᵢ observations,respectively. (12%)

6. The manager of a convenient store wants to know whether the customer arrival in every ten-minute period follows Poisson distribution. The alternatives are as follows:H₀: The population distribution is Poisson.H₁: The population distribution is not Poisson.One day he observes from 8 a.m. to 4 p.m. The data on the number of customers (X) arriving at his store in each ten-minute period are as follows:Hence the sample mean = 6.0.Using the Chi-square procedure, for α = 0.05, test whether the probability distribution of the ten-minute customer arrival is Poisson. (20%)

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