Reading Questions for Chapter 3

Reading and Comprehension Questions for Chapter 4 1. Continuous random variables take on discrete values. True

False

False – see Section 4-1. 2. The probability density function of a continuous random variable is a simple description of the probabilities associated with the random variable. True

False

True – see Section 4-2.

3. The sum of all of the probabilities associated with each specific value of a continuous random variable equals unity. True

False

False – see Section 4-2.

4. The cumulative distribution function of a continuous random variable is the probability that the random variable X is greater than or equal to x, where x is a specific value of the continuous random variable X. True

False

False – see Section 4-3.

5. A cumulative distribution function can be used to find the probability density function of a discrete random variable. True

False

True – see Section 4-3.

6. The mean of a continuous random variable is its expected value. True

False

True – see Section 4-4.

7. The standard deviation of a continuous random variable is its expected value. True

False

False – see Section 4-4. 8. The variance of a discrete random variable is defined as   2



 (x  )

2

f ( x)dx .



True

False

True – see Section 4-4. 9. The variance of a continuous random variable can be written as either

  2



 (x  )

2

f ( x)dx or   2



True



x

2

f ( x)dx   2 .



False

True – see Section 4-4. 10. If X is a continuous uniform random variable defined over the range 10 to 20, the mean of X is: a. 12 b. 15 c. 16 d. None of the above Answer is b; see Equations 4-7. 11. The normal distribution has two parameters; the mean μ, and the variance σ2. True

False

True – see Section 4-6.

12. The standard normal distribution has both mean and variance equal to unity. True

False

False – see Section 4-6.

13. If X is a normal random variable that has mean μ = 20 and standard deviation σ = 2, the standardized value of X = 16 is a. 4 b. -2 c. 2 d. -4 e. None of the above Answer is b; see Equation 4-10 14. To standardize a normal random variable that has mean μ and variance σ2 we used the X  formula Z  . 2 True

False

False – see Equation 4-10. 15. The normal distribution can be used to approximate the binomial distribution if np and n(1-p) are greater than five. True

False

True – see Section 4-7. 17. The exponential random variable models the distance between successive events in a Poisson process. True

False

True – see Section 4-8. 18. In the exponential distribution with parameter λ, the mean and variance are both equal to λ. True

False

False – see Equation 4-15. 19. The exponential distribution has a lack of memory property. True

False

True – see Section 4-8.

20. The Erlang and exponential distributions are special cases of the gamma distribution. True False True – see section 4-9.

21. The Weibull distribution is often used to model the time to failure in reliability engineering work. True

False

True – see Section 4-10.

22. A random variable that is the natural logarithm of a normal random variable is called a lognormal random variable. True

False

True - see Section 4-11.