# Thread: Statistics Random Discreat Variable HWK

1. ## Statistics Random Discreat Variable HWK

I need help aspa on this... I have no idea what to do on it

Sam is 6 years old and Ruth is 4.
To calculate their weekly pocket money they each select a coin at random from a bag containg 7 ten pence coins and 3 twenty pence coins.
Their pocket money is calculated by multiplying the value of their coin by their age, and then adding twice their age.
Find how much each child can expect to receive each week.

if its any help the answers are Sam 90 pence and Ruth 60 pence

thanks

2. Originally Posted by sashywashy
I need help aspa on this... I have no idea what to do on it

Sam is 6 years old and Ruth is 4.
To calculate their weekly pocket money they each select a coin at random from a bag containg 7 ten pence coins and 3 twenty pence coins.
Their pocket money is calculated by multiplying the value of their coin by their age, and then adding twice their age.
Find how much each child can expect to receive each week.

if its any help the answers are Sam 90 pence and Ruth 60 pence

thanks
Let X be the random variable value of chosen coin and let M be the random variable money child gets. Let A be the age of the child.

Then $M = AX + 2A$ and so $E(M) = A E(X) + 2A$.

Assuming replacement of coin, Pr(X = 10 pence) = 7/10 and Pr(X = 20 pence) = 3/10.

Calculate E(X).

Substitute child's age and value of E(X) into E(M).

3. oh thank you
makes so much more sense than the random scraw I was getting