MAT 119 8.1 Distributions of Random Variables
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TUTORIAL WITH WORK SHOWN FOR THE FOLLOWING QUESTIONS
 A coin is tossed four times. Let the random variable X denote the number of tails that occur.
(a) List the outcomes of the experiment.
(b) Find the value assigned to each outcome of the experiment by the random variable X.
(c) Find the event consisting of the outcomes to which a value of 0 has been assigned by X.

Cards are selected one at a time without replacement from a wellshuffled deck of 52 cards until an ace is drawn. Let X denote the random variable that gives the number of cards drawn. What values may X assume?
 Consider the following.
X = The number of times a die is thrown until a 2 appears
Give the range of values that the random variable X may assume.
Classify the random variable as one of the following.
finite discrete
infinite discrete
continuous
 Consider the following.
X = The number of defective iPods in a sample of eight iPods
Give the range of values that the random variable X may assume.
Classify the random variable as one of the following.
finite discrete
infinite discrete
continuous
 Consider the following.
X = The number of hours a child watches television on a given day
Give the range of values that the random variable X may assume.
Classify the random variable as one of the following.
finite discrete
infinite discrete
continuous
 Find conditions on the numbers a and b such that the table gives the probability distribution of the random variable X.
x ?1 0 1 2 4 5
P(X = x)0.2a0.10.1b0.4
a + b =
 The probability distribution of the random variable X is shown in the accompanying table.
x ?5 ?3 ?2 0 2 3
P(X = x) 0.18 0.12 0.34 0.16 0.10 0.10
Find the following.
(a) P(X ? 0)
(b) P(X ? ?3)
(c) P(?2 ? X ? 2)
(d) P(X = ?2)
(e) P(X > 0)
(f) P(X = 1)

An examination consisting of ten trueorfalse questions was taken by a class of 100 students. The probability distribution of the random variable X, where X denotes the number of questions answered correctly by a randomly chosen student, is represented by the accompanying histogram. The rectangle with base centered on the number 8 is missing. What should be the height of this rectangle?
 The Public Housing Authority in a certain community conducted a survey of 1000 families to determine the distribution of families by size. The results are given below.
Family Size 2 3 4 5 6 7 8
Frequency of
Occurrence 300 201 200 101 69 13 116
(a) Find the probability distribution of the random variable X, where X denotes the number of people in a randomly chosen family. (Enter your answers to three decimal places.)
Family Size2345678
Freq3002012001016913116
(b) Draw the histogram corresponding to the probability distribution found in part (a).
(c) Find the probability that a family chosen at random from those surveyed has more than five members. (Enter your answer to three decimal places.)
 The interest rates paid by 30 financial institutions on a certain day for money market deposit accounts are shown in the accompanying table.
Rate, % 3 3.25 3.55 3.56 3.58 3.60 3.65 3.85
Institutions 3 6 7 2 1 7 2 2
Let the random variable X denote the interest rate per year paid by a randomly chosen financial institution on its money market deposit accounts. (Round your answers to three decimal places.)
(a) Find the probability distribution associated with these data.
Rate, %InstitutionsP(X=x)
33
3.256
3.557
3.562
3.581
3.67
3.652
3.852
(b) Find the probability that the interest rate paid by a financial institution chosen at random is less than 3.56% per year.