Stat 245 Recitation 11

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Stat 245 Recitation 11. 10/25/2007 EA 285 10:30am TA: Dongmei Li. Announcement. I can add 2 points to your Exam 1 if you marked “F” on True/False question No.9 in version A and question No.10 in version B.

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### Stat 245 Recitation 11

10/25/2007

EA 285 10:30am

TA: Dongmei Li

Announcement
• I can add 2 points to your Exam 1 if you marked “F” on True/False question No.9 in version A and question No.10 in version B.
• Homework 6 is due on Monday (Oct.29) in lecture. It include following questions from chapter 7: 7.8, 7.14, 7.18, 7.40, 7.42, 7.50, 7.52, and 7.56.
Highlights in Chapter 7
• Random variable
• A numerical variable whose value depends on the outcome of a chance experiment is called a random variable.
• Discrete random variable
• Its set of possible values is a collection of isolated points on the number line.
• Continuous random variable
• Its set of possible values includes an entire interval on the number line.
Highlights in Chapter 7
• The probability distribution of a discrete random variable x gives the probability associated with each possible x value.
• Properties of discrete probability distribution
• For every possible x value, 0p(x) 1
•  p(x) =1
Problem Solving-Chapter 7
• 7.9 Let y denote the number of broken eggs in a randomly selected carton of one dozen eggs. Suppose that the probability distribution of y is as follows:
• Y 0 1 2 3 4
• P(y) .65 .20 .10 .04 ?
• a. What is P(4)?
• b. How do you interpret P(1) = .20?
• c. Calculate P (y  2) and interpret it.
• d. Calculate P (y< 2). Why it is smaller than P (y  2) ?
• e. What is the probability that the carton contains exactly 10 unbroken eggs?
• f. What is the probability that at least 10 eggs are unbroken?
Problem Solving-Chapter 7
• 7.12 Suppose that a computer manufacturer receives computer boards in lots of five. Two boards are selected from each lot for inspection. We can represent possible outcomes of the selection process by pairs. For example, the pair (1, 2) represents the selection of Boards 1 and 2 for inspection.
• a. List the 10 different possible outcomes.
• b. Suppose that Boards 1 and 2 are the only defective boards in a lot of five. Two boards are to be chosen at random. Define x to be the number of defective boards observed among those inspected. Find the probability distribution of x.
Highlights in Chapter 7
• A probability distribution for a continuous random variable x is specified by a density function f(x)
• Two requirements for f(x)
• 1. f(x)  0
• 2. The total area under the density curve is equal to 1.
Problem Solving-Chapter 7
• 7.41 To assemble a piece of furniture, a wood peg must be inserted into a predrilled hole. Suppose that the diameter of a randomly selected peg is random variable with mean 0.2 in. and standard deviation 0.006 in. and that the diameter of a randomly selected hole is a random variable with mean 0.253 in. and standard deviation 0.002 in. Let X1 = Peg diameter, and let X2 = denote hole diameter.
• a. Why would the random variable y, defined as y=x2-X1, be of interest to the furniture manufacturer?
• b. What is the mean value of the random variable y?
• c. Assuming that X1 and X2 are independent, what is the standard deviation of y?
• d. Is it reasonable to think that x1 and X2 are independent? Explain.
• e. Based on your answers to part (b) and (c), do you think that finding a peg that is too big to fit in the predrilled hole would be a relatively common or a relatively rare occurrence? Explain.