Ch. 7 Mind Map
Random Variables
7.1 Discrete and continuous variables
1) Define a discrete variable and a continuous variable.
Discrete
Continuous
Example of type of graph
Example of type of graph
2) Which type a variable would be most appropriate for the following?
a) Fuel economy of a car
d) Distance javelin is thrown
c) Number of parking citations issued by Mr. E in a given
e) Number of students absent on January 14th
day
3) How is P(X= 2) different for continuous verse discrete?
b) Answer the following for both distributions
P(x = 1)
P(x < 1)
P(x ≤ 1)
Continuous
X
P(X)
Discrete
0
.5
7.2 Means and Variances of Random Variables
4) How would you use  x 
xi pi with the discrete distribution given?

Write out the complete calculation.
5) How would you use  x
2
  xi   x  pi with the distribution given?
2
Write out the complete calculation.
6) State the rules for means
State the rules for variances
7) Write Independent next to the rules where X and Y must be independent?
8) Apply the formula y = 3x + 5 to the following
 x  25
and
 x  2.78 .
1
.3
3
.2
Random Review
1) 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
a) Only y values of 0, 1, 2, 3, and 4 have probabilities greater
P(y)
.65
.20
.10
.04
then zero; what is p(4)?
b) How would you interpret p(1) = .20
c) Calculate P( y ≤ 2) and calculate P( y < 2). Explain the difference in terms of eggs.
2) An express mail service charges a special rate for any package that weighs less than 1 lb. Let x denote the weight of a
randomly selected parcel. The probability distribution of x is specified by the following curve.
a) What has to be true about density curves?
b) What is the probability that the package weight is at most 0.5?
(A trapezoid = base*average of two sides)
c) P(X= 2)
3) A student took a national aptitude tests. The scores were normally distributed with the national
average and standard deviations were 475 and 100, respectively.
a) The student scored 625, what percentile does he fall?
b) What score would he need to be in the top 5%?
4) Consider a large ferry that can accommodate cars and buses. The toll for a cars is $3, and the toll for buses is $10. Let x be
the number of cars and y be buses, carried on a single trip. Cars and buses are accommodated on different levels of the ferry
so they are independent of one another. Suppose that x and y have the following probability distributions
x
0
1
2
3
4
5
p(x)
.05
.10
.25
.30
.20
.10
y
0
1
2
p(y)
.50
.30
.20
Compute the mean and standard deviation for x. μx=2.8 σx=1.288
Compute the mean and standard deviation for y.
What is the average fare collected from cars?
What is the average fare collected from both types of vehicles?
5) A multiple-choice exam consists of 50 questions. Each question has five choices, of which only one is correct. Suppose
that the total score on the exam is computed as
y  x1  1 x 2 where x1= number of correct responses and where x2=
4
number of incorrect responses.
a) It can be shown that if a totally unprepared student answers all 50 questions by just selecting one of the five answers
randomly, then  x1  10 and  x2  40 . What is the mean value of the total score, y? Does this surprise you? Explain.
b) Explain why it is unreasonable to use the formulas given in this section to compute the variance or standard deviation of y.