Knowing that the expected number of devices sold per week is exactly 3, what is the value of k?

[takvya]

Hi. I'm Takuya and I'm new here.

A shopkeeper keeps extensive records of the daily sales of a certain device. With the data collected, he constructed the following probability distribution of the random variable X = number of devices sold per week:



Knowing that the expected number of devices sold per week is exactly 3, what is the value of k?

a) 0,05 | b) 0,10 | c) 0,15 | d) 0,25 | e) 0,35

I know that the P line has to be 1, so k + w = 0,35, but I don't know how to calculate k and w isolated.

 

[nasi112]

expected number [MATH] = 0 \cdot 0.05 + 1 \cdot k + 2 \cdot 0.25 + 3 \cdot w + 4 \cdot 0.2 + 5 \cdot 0.15 = 3[/MATH]
and you know that

[MATH]k + w = 0.35[/MATH]
you have two equations and two unknowns

Can you find [MATH]k[/MATH] and [MATH]w[/MATH]?

 

[takvya]

expected number [MATH] = 0 \cdot 0.05 + 1 \cdot k + 2 \cdot 0.25 + 3 \cdot w + 4 \cdot 0.2 + 5 \cdot 0.15 = 3[/MATH]
and you know that

[MATH]k + w = 0.35[/MATH]
you have two equations and two unknowns

Can you find [MATH]k[/MATH] and [MATH]w[/MATH]?

I've tried this:
Letter A:
k = 0,05 and w = 0,30

E(X) = 0,05 + 0,5 + 0,9 + 0,8 + 0,75
E(X) = 3

So is letter A the correct alternative?

 

[nasi112]

I've tried this:
Letter A:
k = 0,05 and w = 0,30

E(X) = 0,05 + 0,5 + 0,9 + 0,8 + 0,75
E(X) = 3

So is letter A the correct alternative?

Yup, that is a correct answer.