Question

Five green balls and 3 white balls are placed in two boxes A and B so that each box contains 4 balls. At each stage, a ball is drawn at random from each box and the two balls are interchanged. Let X(n) denote the number of white balls in box A after the nth draw. Determine the state space and index set. [1+1 = 2 marks] If Y(n) is the total number of green balls in box A after the nth draw, then determine the state space and index set for Y(n) [1.5+1.5 = 3 marks]

Name: five green balls and 3 white balls are placed in two boxes a and b so that each box contains 4 balls at each stage a ball is drawn at random from each box and the two balls are interchanged 91534
Uploaded: 2022-10-10T13:09:56-08:00
Duration: 1 min 7 s
Channel: Sri K
Description: five green balls and 3 white balls are placed in two boxes a and b so that each box contains 4 balls at each stage a ball is drawn at random from each box and the two balls are interchanged 91534

          Five green balls and 3 white balls are placed in two boxes A and B so that each box contains 4 balls. At each stage, a ball is drawn at random from each box and the two balls are interchanged. Let X(n) denote the number of white balls in box A after the nth draw.
Determine the state space and index set. [1+1 = 2 marks]
If Y(n) is the total number of green balls in box A after the nth draw, then determine the state space and index set for Y(n) [1.5+1.5 = 3 marks]

Added by Joyce M.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sri K

10/10/2022

Step 1

The state space for X(n) represents all possible values of the number of white balls in box A after the nth draw. Since there are initially 3 white balls and 5 green balls distributed in two boxes with 4 balls each, the minimum number of white balls in box A can Show more…

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Five green balls and 3 white balls are placed in two boxes A and B so that each box contains 4 balls. At each stage, a ball is drawn at random from each box and the two balls are interchanged. Let X(n) denote the number of white balls in box A after the nth draw. Determine the state space and index set. [1+1 = 2 marks] If Y(n) is the total number of green balls in box A after the nth draw, then determine the state space and index set for Y(n) [1.5+1.5 = 3 marks]