Question

Cans of soda cost $0.30 in a certain vending machine. What is the expected value and variance of daily revenue from that machine, if X is the number of cans sold per day, R is daily revenue, E{X}=125 and σ2 {X}=50

Answer 1

Answer:

The expected revenue is $37.50 and the variance of the revenue is $4.50.

Step-by-step explanation:

The random variable X is defined as the number of cans of soda sold per day.

The expected number of cans sold per day is:

E (X) = 125

The variance of the number of cans sold per day is:

V (X) = 50

The cost of one can of soda is:

Cost of X = $0.30

The formula to compute the expected revenue is:

$E(R)=Cost\ of\ X\times E(X)$

The formula to compute the variance of the revenue is:

$V(R)= (Cost\ of\ X)^{2} \times V(X)$

Compute the expected revenue as follows:

$E(R)=Cost\ of\ X\times E(X)\\= 0.30\times 125\\=37.5$

Thus, the expected revenue is $37.50.

Compute the variance of the revenue as follows:

$V(R)= (Cost\ of\ X)^{2} \times V(X)\\=(0.30)^{2}\times 50\\=4.5$

Thus, the variance of the revenue is $4.50.