4.6 An attendant at a car wash is paid according to the number of cars that pass through. Suppose the probabilities are 1/12, 1/12, 1/4, 1/4, 1/6, and 1/6, respectively, that the attendant receives $7, $9, $11, $13, $15, or $17 between 4:00 P. M. and 5:00 P. M. on any sunny Friday. Find the attendant’s expected earnings for this particular period.

4.7 By investing in a particular stock, a person can make a proﬁt in one year of $4000 with probability 0.3 or take a loss of $1000 with probability 0.7. What is this person’s expected gain?

4.10 Two tire-quality experts examine stacks of tires and assign a quality rating to each tire on a 3-point scale. Let X denote the rating given by expert A and Y denote the rating given by B. The following table gives the joint distribution for X and Y .

4.12 If a dealer’s proﬁt, in units of $5000, on a new automobile can be looked upon as a random variable X having the density function

fx= 21-x,0<x<10,elsewhere

ﬁnd the average proﬁt per automobile.

4.14 Find the proportion X of individuals who can be expected to respond to a certain mail-order solicitation if X has the density function.

fx= 2(x+2)50<x<10,elsewhere

4.28 Consider the information in Exercise 3.28 on page 93. The problem deals with the weight in ounces of the product in a cereal box, with
fx= 25,23.75 ≤x ≤26.250,elsewhere.

4.33 Use Deﬁnition 4.3 on page 120 to ﬁnd the variance of the random variable X of Exercise 4.7 on page 117.
4.7 By investing in a particular stock, a person can make a proﬁt in one year of $4000 with probability 0.3 or take a loss of $1000 with probability 0.7. What is this person’s expected gain?

4.37 A dealer’s proﬁt, in units of $5000, on a new automobile is a random variable X having the density function given in Exercise 4.12 on page 117. Find the variance of X. 4.12 If a dealer’s proﬁt, in units of $5000, on a new automobile can be looked upon as a random variable X having the density function...

...more than 0.1?
2. The following is the probability distribution function of the number of complaints a customer manager has to handle in half an hour.
Suppose he can handle at most 3 complaints in half an hour.
a. What is k?
b. What is the probability there are less than 2 complaints in half an hour?
c. What is the probability there are less than 2 complaints in an hour?
3. A randomvariable [pic] can be assumed...

...SIDS31081 - Statistics Refresher
2006 – 2007
Exercises
(Probability and RandomVariables)
Exercise 1
Suppose that we have a sample space with five equally likely experimental outcomes :
E1,E2,E3,E4,E5.
Let
A = {E1,E2}
B = {E3,E4}
C = {E2,E3,E5}
a. Find P(A), P(B), P(C).
b. Find P(A U B) . Are A and B mutually exclusive?
c. Find Ac, Bc, P(Ac), P(Bc).
d. Find A U Bc and P(A U Bc)
e. Find P(B U C)
Exercise 2
A committee with two members is to be...

...continuous randomvariable because the time is being measured. All possible results for the variable time (t) would be greater than > 0.
b) The weight of a T-bone steak is a continuous randomvariable because the weight of the steak is measured. All the possible results for the weight of the T-bone steak would be positive numbers making the variable weight (w) > greater than 0....

...be infected?
The probability that Alice’s RSA signature on a document is forged is () What is the probability that out of 4 messages sent by Alice to Bob at least one is not forged?
Event A is selecting a “red” card from a standard deck at random. Suggest another event (Event B) that is compatible with Event A.
What is the probability of getting 6 tails in 10 trials of tossing a coin? Solve this problem by using :The approximation mentioned in Theorem 6
The...

...THE MOMENTS OF A RANDOMVARIABLE
Definition: Let X be a rv with the range space Rx and let c be any known constant. Then the kth moment of X about the constant c is defined as
Mk (X) = E[ (X c)k ]. (12)
In the field of statistics only 2 values of c are of interest: c = 0 and c = . Moments about c = 0 are called origin moments and are denoted by k, i.e., k = E(Xk ), where c = 0 has been inserted...

.............................................
.........................................................................
Turn over
2206-7303
0516
–6–
5.
M06/5/MATME/SP1/ENG/TZ2/XX
The probability distribution of the discrete randomvariable X is given by the following table.
x
1
2
3
4
5
P ( X = x)
0.4
p
0.2
0.07
0.02
(a)
Find the value of p.
(b)
Calculate the expected value of X....

...Answer: .5006
. Question 5 .5 out of 5 points
An automotive center keeps tracks of customer complaints received each week. The probability distribution for complaints can be represented as a table or a graph, both shown below. The randomvariable xi represents the number of complaints, and p(xi) is the probability of receiving xi complaints.
xi
0
1
2
3
4
5
6
p(xi)
.15
.1
.28
.20
.10
.10
.07
What is the expected number of...

...Chapter - Section | Problem(s) |
5 – 2 | 10, 14 |
5 – 3 | 12, 32 |
5 – 4 | 18 |
5-2 #10,14
10. Eye Color Groups of five babies are randomly selected. In each group, the randomvariable x is the number of babies with green eyes (based on data from a study by Dr. Sorita Soni at Indiana University). (The symbol 0+ denotes a positive probability value that is very small).
X | P(x) |
0 | .528 |
1 | .360 |
2 | .098 |
3 | .013 |
4 | .001 |
5 | 0+ |...

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