Mathematical Expectation

Question 4.53

Suppose that a grocery store purchases 5 cartons of skim milk at the wholesale price of $1.20 per carton and retails the milk at $1.65 per carton After the expiration date, the unsold milk is removed from the shelf and the grocer receives a credit from the distributor equal to 3/4 of the wholesale price. If the probability distribution of the random variable X, the number of cartons that are sold from this lot is:

x	1	2	3	4	5
f(x)	1/15	2/15	3/15	4/15	5/15

Find the Expected Profit.

Random Variables and Probability Distribution

Question 3.32

The proportion of the budgets for a certain type of industrial company that is allocated to environmental and pollution control is coming under scrutiny. A data collection project determines that the distribution of these proportions is given by:

f (y) = 5 (1-y)^4,  0<=y<=1
          0, elsewhere

a) Verify that the above is a valid density
b) What is the probability that a company chosen at random expends less than 10% of its budget on environmental and pollution controls ?
c) What is the probability that a company selected at random spends more than 50% on environmental and pollution control ?

Probability

Question 2.26

A California study concluded that by following 7 simple health rules a man's life can be extended by 11 years n the average and a woman's life by 7 years. These 7 rules are as follows: no smoking, regular exercise, use alcohol moderately, get 7-8 hours of sleep, maintain proper weight, eat breakfast, and do not eat between meals. In how many ways can a person adopt five of these rules to follow
a) If the person presently violates all 7 rules?
b) If the person never drinks and always eats breakfast?

Probability

1. In how many different ways can a true-false test consisting of 9 questions be answered ?


2. A pair of dice is tossed. Find the probability of getting
a) a total of 8.
b) at most a total of 5.