Find the mean perimeter.

1.  The four sides of a picture frame consist of two pieces selected from a population whose mean length is 30 cm with standard deviation 0.1 cm, and two pieces selected from a population whose mean length is 45 cm with standard deviation 0.3 cm a.  Find the mean perimeter. b.  Assuming the four pieces […]

What is the standard deviation of the total length?

1.  A certain commercial jet plane uses a mean of 0.15 gallons of fuel per passenger-mile, with a standard deviation of 0.01 gallons. a.  Find the mean number of gallons the plane uses to fly 8000 miles if it carries 210 passengers. b.  Assume the amounts of fuel used are independent for each passenger-mile traveled. […]

Find the marginal probability mass function pY (y).

1.  The number of bytes downloaded per second on an information channel has mean 10 5 and standard deviation 10 4 . Among the factors influencing the rate is congestion, which produces alternating periods of faster and slower transmission. Let X represent the number of bytes downloaded in a randomly chosen five-second period.   a.  […]

Find the conditional probability mass function pY|X (y | 2)

1.  Refer to Exercise 1. a.  Find the conditional probability mass function pY|X (y|0). b.  Find the conditional probability mass function pX|Y (x|1). c.   Find the conditional expectation E(Y | X = 0). d.  Find the conditional expectation E(X | Y = 1).   2.  Refer to Exercise 4. a.  The total number of assemblies […]

Find the conditional probability mass function pY\X (y | 4)

1.  Refer to Exercise 4. Assume that the cost of repairing an assembly whose clearance is too little is $2, and the cost of repairing an assembly whose clearance is too much is $3. a.  Express the total cost of repairs in terms of X and Y. b.  Find the mean of the total cost […]