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Advanced Probability and Statistical Distributions: A Comprehensive Assignment

Study of probability distributions and statistical models in-depth.

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    Advanced Probability and Statistical Distributions: A Comprehensive Assignment Question 1 a. Carl arriving first F x,y (x,y) = P(X < x, Y < y) F x,y (x,y) = P(X < x,Y < y) P(X=x, Y=y) x - c(2,0,3) n - 3 p - c(1/3,1/3,1/3) P(X 1 =2, X 2 =0, X 3 =3) whereby X=(X 1 ,X 2 ,X 3 ) ~ Mult 3 (5,(1/3,1/3,1/3)) The probability is 1/3 Question b. =1 - (1/3 + 1/3 +1/3) = 0.1 Question c. Ans. 1/3 Question d.

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    1*1/2 + ½ - ½ Ans 1/2 Question 2. Assuming Y is a normal distribution E(Y/k) is the conditional mean for Y with x linear in x and Var(Y/k) is the conditional variance The conditional variance of the conditional distribution is Y given X=x Assuming X is a normal distribution. The PDF is

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