examThreeReview

I n x xy on d x 2 1 y 2 j o x xy 3 on d x 2 1 y 2 4

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(i) n ( x ) = xy on D = { 0 x 2; 1 y 2 } (j) o ( x ) = xy 3 on D = { 0 x 2; 1 y 2 } 4. Determine the value of k which makes the following functions are (joint) probability density functions over the indicated intervals. (a) f ( x ) = k on [1 , 5]. (b) g ( x ) = k x 2 on [1 , 3]. (c) h ( x ) = k sin x on [0 , π ]. (d) i ( x ) = ke 3 x on [0 , ln 2]. (e) j ( x ) = ke x/ 2 on [0 , ). (f) l ( x ) = k x (2 - y ) on D = { 0 x 1; 1 y 2 } .
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(g) m ( x ) = k ( x - x 3 ) e 2 y on D = { 0 x 1; 0 y < ln 4 } . (h) n ( x ) = k (2 - 2 x - y + xy ) on D = { 0 x 1; 1 y 2 } . 5. Given that f ( x ) is a (joint) probability density function, find the indicated probabilities. iii. P ( x = 2) iv. P ( x < 2) braceleftBigg x if 0 x 1 2 - x if 1 x 2 i. P ( 1 2 x 1) ii. P ( 1 2 x 3 2 ) iii. P ( x 1) iv. P ( x 3 2 ) iii. P ( x = 50) iv. P ( x 2)
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