## Find the probability mass function of X

1.  Determine whether each of the following random variables is discrete or continuous.

a.  The number of heads in 100 tosses of a coin.

b.  The length of a rod randomly chosen from a day's production.

c.   The final exam score of a randomly chosen student from last semester's engineering statistics class.

d.  The age of a randomly chosen Colorado School of Mines student.

e.  The age that a randomly chosen Colorado School of Mines student will be on his or her next birthday.

2.   A survey of cars on a certain stretch of highway during morning commute hours showed that 70% had only one occupant, 15% had 2, 10% had 3, 3% had 4, and 2% had 5. Let X represent the number of occupants in a randomly chosen car.

a.  Find the probability mass function of X

b.  . Find P(X ≤ 2).

c.   Find P(X > 3).

d.  Find μX .

e.  Find σX .

### What is the probability that the parcel was shipped express and arrived the next day?

1.  In a lot of n components, 30% are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective,….

### Given that the test is positive, what is the probability that the person has the disease?

1.  Refer to Exercise 28. Assume that both inspectors inspect every item and that if an item has no flaw, then neither inspector will detect a flaw. a.  Assume that….

### If a man tests negative, what is the probability that he actually has the disease?

1.  Refer to Example 2.26. a.  If a man tests negative, what is the probability that he actually has the disease? b.  For many medical tests, it is standard procedure….