Question

please answer i only have 3-4 minutes !!!

On any given day, a bike shop sells either 0, 1, 2, or 3, bikes, with probabilities 0.3, 0.4, 0.2, and 0.1 respectively.

Suppose they make a profit of $400 from each bike sold, but they have a fixed cost of $400 per day for rent and salaries at the small dealer.

Let the random variable X = the net profit per day. (i.e., the profit from the sale of bicycles minus the fixed cost).

a) Develop a probability distribution for the net profit per day. What are the X and f(x) values?

b) Show that your probability distribution satisfies the conditions for a discrete probability distribution. In other words, describe in words why the probability distribution that you created is a valid one.

c) Calculate the expected value of the probability distribution. Interpret what this means in words.

Answer 1

(a)

Corresponding calculations are as follows.

Thus probability distribution for the net profit per day is as follows.

In the distribution,

• X takes values of net profit (in dollar) per day i.e. -400, 0, 100 and 800.
• f(x) is same as P(X=x) which denotes corresponding probabilities of  net profit.

(b)

We observe as follows.

• There are probabilities corresponding to discrete points only.
• Sum of probabilities is 1, which is essential in case of discrete probability distribution.

Thus the conditions for a discrete probability distribution are satisfied and the probability distribution that we constructed is a valid one.

(c)

Expected value of the probability distribution is given by

This expected value interprets that, in long run average profit per day is $40.