Asked by MW
Five chips numbered 1-5 are placed in a jar. Two chips are drawn.
Let Z= the sum of the numbers.
WHat is the expected value of the random variable?
I know I have to use E = np
Can someone explain?
Let Z= the sum of the numbers.
WHat is the expected value of the random variable?
I know I have to use E = np
Can someone explain?
Answers
Answered by
drwls
Add up the sum of the products of the sum and the probability of that sum.
Possible sums are 3,4,5,6,7,8 and 9.
There are 2 ways to get 3 or 9:
(1,2)(2,1); (4,5), (5,4)
There are 2 ways to get 4 or 8
There are 4 ways to get 5 or 7:
(1,4)(4,1)(2,3)(3,2); (2,5)(5,2);(4,3)(3,4)
There are 4 ways to get 6:
(1,5)(5,1)(2,4)(4,2)
The probability of getting 3,4,8 or 9 is 1/10. The probability of getting 5,6 or 7 is 1/5.
E = (1/10)(3+4+8+9) + (1/5)(5+6+7)
= 2.4 + 3.6 = 6
Possible sums are 3,4,5,6,7,8 and 9.
There are 2 ways to get 3 or 9:
(1,2)(2,1); (4,5), (5,4)
There are 2 ways to get 4 or 8
There are 4 ways to get 5 or 7:
(1,4)(4,1)(2,3)(3,2); (2,5)(5,2);(4,3)(3,4)
There are 4 ways to get 6:
(1,5)(5,1)(2,4)(4,2)
The probability of getting 3,4,8 or 9 is 1/10. The probability of getting 5,6 or 7 is 1/5.
E = (1/10)(3+4+8+9) + (1/5)(5+6+7)
= 2.4 + 3.6 = 6