(A) The recent census in a large county revealed the following probability distribution for the number of children under 18 per household.
Number of Children 0 1 2
Number of Households 24,750 37,950 59,400
Number of Children 3 4 5
Number of Households 29,700 9,900 3,300
a.Develop the probability distribution of X, the number of children under 28 per household.
b.Determine the following probabilities.
(B) We are given the following probability distribution.
x 0 1 2 3
P(X) .1 .3 .2 .4
a. Calculate the mean, variance, and standard deviation.
b. Suppose that Y=3X+2. For each value of X, determine the value of Y. Whatis the probability distribution of Y?
c. Calculate the mean, variance, and standard deviation from the probability distribution of Y.
d. Use the laws of expected value and variance to calculate the mean, variance, and standard deviation of Y from the mean, variance, and standard deviation of X. Compare your answers in parts c and d. Are they the same(except for rounding)?
(C) The owner of a small firm has just purchased a personal computer, which the expects will serve herfor the next 2 years. The owner has been told that she "must" buy a surge suppressor to provide protection for her new hardware against possible suges or variations in the electrical current, which have the capacity to damage the computer. The amount of damage to the computer depedns on the strength of the surge. It has been estimated that there is a 1% chance of incurring $400 damage, a 2% chance of incurring $200damage, and a 10% chance of $100 damage. An inexpensive suppressor, which wouldprovide protection for only one surge, can be purchased. How much should the owner be willing to pay if she makes decisions on the basis of expected value?