Controlling the water hyacinth. An insect that naturally feeds on the water hyacinth...

Controlling the water hyacinth. An insect that naturally feeds on the water hyacinth, one of the world’s worst aquatic weeds, is the delphacid. Female delphacids lay anywhere from one to four eggs onto a water hyacinth blade. The Annals of the Entomological Society of America (Jan. 2005) published a study of the life cycle of a South American delphacid species. The following table gives the percentages of water hyacinth blades that have one, two, three, and four delphacid eggs:

a. One of the water hyacinth blades in the study is randomly selected, and x, the number of delphacid eggs

on the blade, is observed. Give the probability distribution of x.

b. What is the probability that the blade has at least three delphacid eggs?

c. Find E(x) and interpret the result.