Reference: Probabilits et statistique, M'hammed Mountassir. Seconde dition dition Modulo.

Course: MAT2375 Probability and statistics

Question:

(To be done with the R software) Either a sample of size 5, X₁,....,X₅ (i.i.d) as a random variable X that gives the score in mathematics normally distributed with an average of X and variance ². Another sample of size 8, Y₁,....,Y₈ (i.i.d) as a random variable Y that gives the score in language normally distributed with

A mean of Y and variance ².

(A) Use the following data to verify the normality of the data and if we can assume that the 2 variables have unknown variances but can be assumed equal or not. (b) Depending on your answer to the question (a) find a 90% knowledge interval for_XY:

x₁= 644; x₂= 493; x₃= 532; x₄ = 462; x₅ = 565 and y₁ = 623; y₂ = 472; y₃ = 492; y₄ = 661; y₅ = 540; y₆ = 502; y₇ = 549; y₈ = 518

Note: D'ont Forget to do with R software. Please