Exercises. 1. Which of the functions sketched in a-d could be a probability density function for a continuous random variable?

1. Which of the functions sketched in a - d could be a probability density function for a continuous random variable? Why or why not?

f (x)

x

b)

2. Determine the following probabilities from the curve diagrammed in exercise 1(a).

a) b)

c) d)

3. For the curve graphed in exercise 1(c) which of the two intervals or is assigned a higher probability?

4. The time it takes for a TV repair master to finish his job (in hours) has a

density function of the form

a) Determine the constant c.

b) What is the probability that a TV repair master will finish the job in less than 75 minutes? Between and 2 hours?

5. Suppose that the loss in a certain investment, in thousands of dollars, is a continuous random variable X that has a density function of the form

a) Calculate the value of k.

b) Find the probability that the loss is at most $500.

6. Let the random variable X has probability density function

a) Draw the probability density function

b) Show that the density function has the properties of a proper probability density function

c) Find the probability that X takes a value between 0.5 and 1.5.

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