Reference no: EM132385054

Question

1. You invest $2000 in a recently introduced stock. Let X represent the return on this investment, in dollars, after one year. Based on historical records of stocks for similar companies, the probability table for X is estimated to be:

X 3000 500 -2000

P(X=x) 0.08 0.63 ???

(a) Find P(X = -2000)

(b) Find E(X). How would you interpret this value?

-2000

(c) Find E(X2).

(d) Use your answers in parts (b) and (c) to find V(X).

2. Also Gang Li has 20 textbooks on his bookshelf, 13 of which are statistics textbooks. He plans to pick 5 textbooks at random to donate to a book sale intended to raise money for the Undergraduate Math Society. Let X represent the number of statistics textbooks out of the 5 books selected. Name the probability distribution of X and explain why this is the case. Identify any relevant parameter values.

3. Jed Clampett, the president of Ozark Oil, plans to conduct a preliminary survey to locate oil deposits. The probability of striking oil at a single location is 0.1, independent of all other locations. If Jed decides to drill for oil at 18 different locations, what is the probability that he will strike oil at between 2 and 4 of these locations, inclusive? To answer this question, you must first define an appropriate random variable, specify its probability distribution, and state the values of any relevant parameters.