9. (a) If X takes non-negative integer values show that E[X] = P[X>n]. n=0 (b) Show...

 

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9. (a) If X takes non-negative integer values show that E[X] = P[X>n]. n=0 (b) Show that b+r+1 b+1 ("+")=("+++). T n+b == b n=0 (c) An urn contains b blue and r red balls. Balls are removed at random until the first blue ball is drawn. Show that the expected number drawn is b++. Hint: Use the result of (a) and (b). 9. (a) If X takes non-negative integer values show that E[X] = P[X>n]. n=0 (b) Show that b+r+1 b+1 ("+")=("+++). T n+b == b n=0 (c) An urn contains b blue and r red balls. Balls are removed at random until the first blue ball is drawn. Show that the expected number drawn is b++. Hint: Use the result of (a) and (b).