tion of two discrete random variables, x and V, is given in the following table
ID: 3336587 • Letter: T
Question
tion of two discrete random variables, x and V, is given in the following table PK) 0.25 0.1 0.1 35 0.4 0.3 0.15 0.25 a) points) Calculat (6 points) Calculate the (3 points) Are X and Y independent Explain. 6 points) Calculate E(X) and E(Y) Explain. cova d) (5 points) Find E(max(x, Y) P (Xu) p 10 JO)-0.1 ney ore nal indepen 0.1+ 0.3+0.15 =6.5s 2. Suppose that the depth (cm) of a bioturbation layer in sediment in a certain region follows a un distribution on the interval [8, 20]. e) (6 points) what are the mean () and variance () of depth? f) (4 points) What is the probability that a random observed depth is at most 10? D- AExplanation / Answer
I am assuming you are asking solution for 2. as 1 is already solved on the image.
2. Depth(cms) of a bioturbutation layer in sediment follows a uniform distribution over the inetrval [8,20]
f(x,a,b) = {1/b-a 8<=x<=10 ; 0 elsewhere
Mean of depth = a+b/2 = 8+10/2 = 9
variance of depth = (b-a)^2/12 = (2)^2/12 = 4/12 = 1/3 = 0.333
P(x <=10) = P(x<8) + P(8<= x <=10) = 0 + 10-8/10-8 = 1
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