Each one of four people will request either coke d let x denote the number that request coke, where the remainder request sprite. the probability distribution of x is given above. (for instance the probability exactly 3 request coke is 0.33) x 0 | 1 | 2 | 3 | 4 or sprite. pcx = x) 0.09 0.15 0.18 0.33 0.25 a) (compute the mean "e(x)" and variance "v(x)": b) if cokes cost $5 each and sprites cost $3 each, then find e(r) and v(r) (mean and variance) where r is the revenue generated from the sale of the four drinks, assuming all get, and pay for, the drink they requested. (hint: write r as a function of x) c) suppose there are only 3 cokes and 3 sprites available. what is the probability that when the four make their orders, everyone gets what they ordered?

a) E(x)=2.5 V(x)=1.59

b) E(R)=17 V(R)=6.36

c) The probability that, when the four make their orders, everyone gets what they ordered is P=0.66.

Step-by-step explanation:

a) The mean E(x) can be calculated as:

The variance V(x) can be calculated as:

b) The revenue can be expressed as:

Then, the expected value of R canbe expressed in function of x:

The expected revenue is $17.

The variance of R is

c) In the case there are only 3 Cokes and 3 Sprites available, the only orders that can not be fullfilled are when X=0 (they order 4 Sprites) and X=4 (they order 4 Cokes).

The probability of these events is:

So, the probability of everyoned getting what they ordered is:

The probability that, when the four make their orders, everyone gets what they ordered is P=0.66.

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