Question

5. An urn contains r + b balls, of which r are red and b are black. They are withdrawn from the urn, one at a time and without replacement. Let X be the number of red balls removed before the first black ball is chosen. We are interested in determining E[X]. To obtain this quantity, number the red balls from 1 to r. Now define the random variables X_i, i = 1, ..., r, by X_i = { 1, if red ball i is drawn before any black ball { 0, otherwise (a) Express X in terms of the X_i. (b) Find E[X]. (c) If instead we defined Y_i = { 1, if red ball is drawn in the ith draw { 0, otherwise could you write X in terms of Y_i?

          5. An urn contains r + b balls, of which r are red and b are black. They are withdrawn from the urn, one at a time and without replacement. Let X be the number of red balls removed before the first black ball is chosen. We are interested in determining E[X]. To obtain this quantity, number the red balls from 1 to r. Now define the random variables X_i, i = 1, ..., r, by

X_i = { 1, if red ball i is drawn before any black ball
      { 0, otherwise

(a) Express X in terms of the X_i.
(b) Find E[X].
(c) If instead we defined

Y_i = { 1, if red ball is drawn in the ith draw
      { 0, otherwise

could you write X in terms of Y_i?

5. An urn contains r + b balls, of which r are red and b are black. They are withdrawn from the urn, one at a time and without replacement. Let X be the number of red balls removed before the first black ball is chosen. We are interested in determining E[X]. To obtain this quantity, number the red balls from 1 to r. Now define the random variables Xi, i = 1, ..., r, by

Xi = 1, if red ball i is drawn before any black ball
0, otherwise

(a) Express X in terms of the Xi.
(b) Find E[X].
(c) If instead we defined

Yi = 1, if red ball is drawn in the ith draw
0, otherwise

could you write X in terms of Yi?

Added by Ronald E.

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