Respuesta :
Answer:
The expected value of the sum of the numbers on the two selected tags is 29.
Step-by-step explanation:
Given : A box contains 10 tags, numbered 1 through 10, with a different number on each tag.
Let [tex]X_1=1[/tex] and [tex]X_2=10[/tex]
A second box contains 8 tags, numbered 20 through 27, with a different number on each tag.
Let [tex]Y_1=20[/tex] and [tex]Y_2=27[/tex]
One tag is drawn at random from each box.
To find : What is the expected value of the sum of the numbers on the two selected tags?
Solution :
The expected value of the sum of the numbers on the two selected tags is given by,
[tex]E(X)=\frac{X_1+X_2}{2}+\frac{Y_1+Y_2}{2}[/tex]
[tex]E(X)=\frac{1+10}{2}+\frac{20+27}{2}[/tex]
[tex]E(X)=\frac{11}{2}+\frac{47}{2}[/tex]
[tex]E(X)=5.5+23.5[/tex]
[tex]E(X)=29[/tex]
Therefore, the expected value of the sum of the numbers on the two selected tags is 29.
The expected value of the sum of the numbers on the two selected tags is 29 and this can be determined by using the given data.
Given :
- A box contains 10 tags, numbered 1 through 10, with a different number on each tag.
- A second box contains 8 tags, numbered 20 through 27, with a different number on each tag.
- One tag is drawn at random from each box.
Given that a box contains 10 tags, numbered 1 through 10, with a different number on each tag, so, let [tex]\rm A_1 = 1[/tex] and [tex]\rm A_{2} = 10[/tex].
Also given that a second box contains 8 tags, numbered 20 through 27, with a different number on each tag, so, let [tex]\rm B_1 = 20[/tex] and [tex]\rm B_2= 27[/tex].
The sum of the numbers on the two selected tags is:
[tex]\rm E(X) = \dfrac{A_1+A_2}{2}+\dfrac{B_1+B_2}{2}[/tex]
[tex]\rm E(X) = \dfrac{1+10}{2}+\dfrac{20+27}{2}[/tex]
E(X) = 5.5 + 23.5
E(X) = 29
The expected value of the sum of the numbers on the two selected tags is 29.
For more information, refer to the link given below:
https://brainly.com/question/23017717
