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℘A,B (a, b) Suppose the random variables A and B have joint PDF given by ℘A,B...

℘A,B (a, b)

Suppose the random variables A and B have joint PDF given by

℘A,B (−1, 0) = 0.10

℘A,B (−1, 1) = 0.05

℘A,B (0, 0) = 0.05

℘A,B (0, 1) = 0.15

℘A,B (0, 2) = 0.05

℘A,B (1, 1) = 0.10

℘A,B (1, 2) = 0.10

℘A,B (2, 0) = 0.20

℘A,B (2, 2) = 0.10

℘A,B (2, 3) = 0.10

a. Find P(−2 ≤ A ≤ 1/2, −1/2 ≤ B < 2)?

b. Find P(A ≤ 1/2)

c. Calculate the marginals ℘A(a) and ℘B(b)?

d. Use the marginal ℘A(a) and find P(A ≤ 1/2).

e. calculate the conditional ℘B | A=2(b)?

f. are A and B are independent or not.

Math   Statistics-And-Probability   
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