The continuous random variables ? and ? have joint density function ? where ?(?, ?) =...

Question

Question

The continuous random variables ? and ? have joint density function ? where ?(?, ?) = { ???(? + ?), 0 ≤ ? ≤ 1; 0 ≤ ? ≤ 1

0, ??ℎ??????

a) Determine the value of the constant ?. [3 marks]

b) Calculate i) ?(? < 2?) [4 marks]

ii) ?(?^2 + ?^2 < 1) [4 marks]

iii) ?((?, ?) ∈ ?), where ? is the region bounded by ? = ? and ? = ?^2 . [4 marks]

c) Calculate ?(? + ?). [3 marks]

d) Are ? and ? independent? Give a reason to support your answer.

Answer 1

Answer #1

Answer 2

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