Reading and Comprehension Questions for Chapter 5
1. The probability distribution that describes the simultaneous behavior of two or more
random variables is called a joint distribution.
True
False
True – see Section 5-1.
2. A marginal probability distribution is the individual probability distribution of one of
the random variables in a joint distribution.
True
False
True – see Section 5-1.2.
3. A conditional probability distribution does not depend on the values of any other
random variables.
True
False
False – see Section 5-1.3.
4. The conditional mean of the random variable Y given that X = x, in the case of discrete
random variables, is found as E (Y | x)   yfY | x ( y ) .
y
True
False
True – see Section 5-1.3.
5. The conditional variance of the random variable Y given that X = x, in the case of
discrete random variables, is found as V (Y | x)   y 2 fY | x ( y ) .
y
True
False
False – see Equations 5-5
6. Two random variables X and Y are independent if f XY ( x, y)  f X ( x) fY ( y) .
True
False
True – see Section 5-1.4.
7. If the set of points in two-dimensional space that receive positive probability under the
joint distribution of X and Y does not form a rectangle, X and Y are independent.
True
False
False – see Section 5-1.4.
8. If X and Y are independent, then fY ( y )  fY | x ( y ) .
True
False
False – see Equations 5-6.
9. The conditional probability mass function is defined as fY | x ( y ) 
True
f XY ( x, y )
.
f X ( x)
False
True – see Section 5-2.3.
10. If X and Y are jointly distributed continuous random variables, the mean and variance
of X cannot be found from the joint distribution.
True False
False – see Section 5-2.5
11. The covariance of two random variables is a measure of the relationship between
them.
True
False
True – see Section 5-3.
12. The covariance between two random variables X and Y is
a. E[(Y   X )(Y  Y )]
b. E ( XY ) 2   X Y
c. E ( XY ) 2  (  X Y ) 2
Answer is a – see Equation 5-26.
13. The correlation between two random variables X and Y is  XY 
True
Cov( X , Y )
.
V ( X )V (Y )
False
True – see Equation 5-27.
14. If X and Y are positively correlated, then there is not a linear relationship between
them.
True
False
False – see Section 5-3.
15. If Y and X are independent random variables, then the correlation between them is
zero.
True
False
True – see Section 5-3.
16. If the correlation between the two Y and X is zero, then the random variables are
independent.
True
False
False – see Section 5-3.
17. The bivariate normal distribution has parameters  X , Y ,  Y2 ,  X2 and  .
True
False
True – see Equation 5-30.
18. If Y and X have a bivariate normal distribution, then the marginal distributions of Y
and X are not necessarily normal.
True
False
False – see Section 5-4.
19. If Y and X are random variables and a and b are constants, then the expected value of
Y = aY +bX is
a.
b.
c.
d.
aE ( X )  bE (Y )
aE ( X )  bE (Y )
E ( X )  E (Y )
E ( X )  E (Y )
Answer is b – see Equation 5-35 for the general case.
20. If Y and X are random variables and a and b are constants, then the variance of Y = aY
+bX is a2Y +a2X .
True
False
True – see Equation 5-37 for the general case.