# Random Variable and Density Function

Topics: Random variable, Probability density function, Probability theory Pages: 3 (868 words) Published: April 2, 2012
4.6 An attendant at a car wash is paid according to the number of cars that pass through. Suppose the probabilities are 1/12, 1/12, 1/4, 1/4, 1/6, and 1/6, respectively, that the attendant receives \$7, \$9, \$11, \$13, \$15, or \$17 between 4:00 P. M. and 5:00 P. M. on any sunny Friday. Find the attendant’s expected earnings for this particular period.

4.7 By investing in a particular stock, a person can make a proﬁt in one year of \$4000 with probability 0.3 or take a loss of \$1000 with probability 0.7. What is this person’s expected gain?

4.10 Two tire-quality experts examine stacks of tires and assign a quality rating to each tire on a 3-point scale. Let X denote the rating given by expert A and Y denote the rating given by B. The following table gives the joint distribution for X and Y .

4.12 If a dealer’s proﬁt, in units of \$5000, on a new automobile can be looked upon as a random variable X having the density function

fx= 21-x,0<x<10,elsewhere

ﬁnd the average proﬁt per automobile.

4.14 Find the proportion X of individuals who can be expected to respond to a certain mail-order solicitation if X has the density function.

fx= 2(x+2)50<x<10,elsewhere

4.28 Consider the information in Exercise 3.28 on page 93. The problem deals with the weight in ounces of the product in a cereal box, with
fx= 25,23.75 ≤x ≤26.250,elsewhere.

4.33 Use Deﬁnition 4.3 on page 120 to ﬁnd the variance of the random variable X of Exercise 4.7 on page 117.
4.7 By investing in a particular stock, a person can make a proﬁt in one year of \$4000 with probability 0.3 or take a loss of \$1000 with probability 0.7. What is this person’s expected gain?

4.37 A dealer’s proﬁt, in units of \$5000, on a new automobile is a random variable X having the density function given in Exercise 4.12 on page 117. Find the variance of X. 4.12 If a dealer’s proﬁt, in units of \$5000, on a new automobile can be looked upon as a random variable X having the density function...

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