Thread: Stats question

For an upcoming concert, each customer may purchase up to 3 child tickets and 3 adult tickets. let C be the number of child tickets purchased by a single customer. The probability distribution of the number of child tickets purchased by a single customer is given below.

----------------------
C |0 |1 |2 |3 |
P(c) |0.4|0.3|0.2|0.1 |
----------------------


A) Compute the mean and standard deviation of c
mean = 1 , and standard deviation = 1 (i think, i did the work on paper)

b) suppose the mean and the standard deviation for the number of adult tickets purchased by a signle customer are 2 and 1.2, respectively. Assume that the number of child tickets and adult tickets purchased are independent random variables. Compute the mean and the standard deviation of the total number of adult and child tickets purchased by a single customer.

c) Suppose each child ticket costs $15 and each adult ticket costs $25. Compute the mean and the standard deviation of the total amount spent per purchase.



Anyone want to help me on on b and c ? I was supposed to have this done for 2morow, And im drawing blanks.

Originally Posted by Bradley55

For an upcoming concert, each customer may purchase up to 3 child tickets and 3 adult tickets. let C be the number of child tickets purchased by a single customer. The probability distribution of the number of child tickets purchased by a single customer is given below.

----------------------
C |0 |1 |2 |3 |
P(c) |0.4|0.3|0.2|0.1 |
----------------------


A) Compute the mean and standard deviation of c
mean = 1 , and standard deviation = 1 (i think, i did the work on paper)

b) suppose the mean and the standard deviation for the number of adult tickets purchased by a signle customer are 2 and 1.2, respectively. Assume that the number of child tickets and adult tickets purchased are independent random variables. Compute the mean and the standard deviation of the total number of adult and child tickets purchased by a single customer.

As the numbers of adult and child tickets sold are independed the mean and variance of their sum is equal to the sum of their means and variances.

(standard deviation is of course the square root of the variance).

c) Suppose each child ticket costs $15 and each adult ticket costs $25. Compute the mean and the standard deviation of the total amount spent per purchase.

Let a and c denote the number of adult and child tickets sold repectivly.
Then 25a and 15c are also independant and so the mean and variance of their sum is the sum of their individual means and variances.

.

Can you work this problem out with me im still lacking the concept a little bit. I have school in 7 hrs, and my teacher said we will have a question like this!

Originally Posted by Bradley55

Can you work this problem out with me im still lacking the concept a little bit. I have school in 7 hrs, and my teacher said we will have a question like this!

You have posted barely 10 minutes or so after the reply by Constatine11. I don't see how you could have given sufficient thought to his/her reply in that time.

What part of the reply are you still drawing a blank on?

You're expected to know that

(b) E(A + C) = E(A) + E(C)

(c) E(25A + 15C) = 25 E(A) + 15 E(C)

and further, if A and C are independent random variables then

(b) Var(A + C) = Var(A) + Var(C)

(c)