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MATH377: Financial And Actuarial Modelling In Rtutorial 5Exercise 1. Let X = (X1, X2) Be A Bivariate Normal Distributed Random Vector With Mean Vector Μ = (1.5, 1) And Covariance Matrixa) Evaluate The Density Function Of X At X = (1, 1) And X = (0, 2).B) Compute P(−2 ≤ X1 ≤ 4, X2 &> 1).C) Plot The 3

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MATH377: Financial And Actuarial Modelling In Rtutorial 4Exercise 1. For The Chi-Squared Distribution (Root Name Chisq):A) Use 3 Degrees Of Freedom To Generate A Sample Of Size 1000.B) Plot A Histogram Of Your Sample In A).C) Write An R Function To Compute The Loglikelihood Function. Test Your Funct

MATH377: Financial And Actuarial Modelling In R Tutorial 1 Exercise 1. Write An R Code To Determine The Result Of The Following Computation:Exercise 2. Without Using R, Determine The Result Of The Following Logical Computation((!(4 == 3) | (Abs(-3) &<= 2)) & ((2^2 &> 4) & (TRUE))) | ((!FALSE | (4+2)...

MATH377: Financial And Actuarial Modelling In R Tutorial 2 Exercise 1. Create Three Vectors Of Length 3, With Content And Names Of Your Choice. Next, Combine The Three Vectors Into A 3 × 3 Matrix Where Each Column Represents One Of Your Vectors. Finally, Compute The Determinant (Det() - Is Your Matr