A target-shooting video game is designed to create rectangles on the screen that are X millimeters wide and Y millimeters tall as (sort of) shown below.  X and Y are random variables with ranges as shown below in the joint pdf after the rectangle. X and Y are independent. Y                                                                        X fXY(x, y) = xy/64   for 3 mm < x < 5 mm and 3 mm < y < 5 mm This question is part of a quiz or exam at Arizona State University.  No portion may not be posted to any website, photos and screenshots may not be taken, and no portion of it may be printed out. Let A be the area of a rectangle generated by this video game.  E(A) = ______ mm2 .  Express your answer to four decimal places.

An engineer has collected processing times for a certain part as follows:  7 min, 13 min, 2 min, 4 min, 4 min, 14 min.  This question is part of a quiz or exam at Arizona State University.  No portion may not be posted to any website, photos and screenshots may not be taken, and no portion of it may be printed out. The table for a normal probability plot would be:   j xj (j-0.5)/n zj 1 A F K 2 B G L 3 C H M 4 D I N 5 E J O 6 P Q R To two decimal places, letter R in the table is equal to  _____. Express your answer to two decimal places.

Thickness measurements of a coating process are made to the nearest tenth of a millimeter. The thickness measurements are have the discrete uniform pmf with values 1.0, 1.1, 1.2. This copywritten question is part of a quiz or exam at Arizona State.  It may not be posted or reproduced without the permission of the author, Dr. L. Chattin, and Arizona State University.  The standard deviation of the thickness is ______ mm. Express your answer to four decimal places.

If X and Y are independent, then _________.  This question is part of a quiz or exam given at Arizona State University, copywritten by Dr. L. Chattin.  It may not be reproduced, posted or distributed without permission of Arizona State University and L. Chattin.   Select the answer that best completes the sentence. 

A ferry in Long Beach, CA makes one trip each day to Catalina Island.  It is scheduled to arrive there at 10:00 am, but in actuality, it is always a little late. Its arrival time (in minutes after 10 am) has the exponential pdf with mean equal to 4 minutes. This copywritten question is part of a quiz or exam at Arizona State.  It may not be posted or reproduced without the permission of the author, Dr. L. Chattin, and Arizona State University. Determine the probability that the ferry arrives after 10:0[x] am on [a] consecutive days (Monday through Friday).  Assume independence. 

An environmental testing station tests 98 parts in sequence.  The probability that a part passes the test is 0.77.  The parts are independent. This copywritten question is part of a quiz or exam at Arizona State University. It may not be posted or reproduced in any way without the permission of Dr. L. Chattin and Arizona State.  If you wanted to determine the probability that fewer than 85 of these parts pass, what is the best definition of the random variable you’d use? Select the answer that best completes the sentence.   “X is  _________________________________________. “

A video game creates random squares, each with side length Y cm. The probability distribution of Y is Continuous Uniform between 1 cm and 2.5 cm. This question is part of a quiz or exam given at Arizona State University, copywritten by Dr. L. Chattin.  It may not be reproduced, posted or distributed without permission of Arizona State University and L. Chattin.  Place your answers in the space below. a. An expression for the area of a square, A,  in terms of Y is ___________ b. The expected value of the area is _______ c. The variance of the area is _______ d. The probability that the area is more than 4 cm2 is ______

Consider the following MGF of random variable, X:   MX(t) = 0.21 + 0.30e2t  +  0.20e4t + 0.29e6t This question is part of a quiz or exam given at Arizona State University, copywritten by Dr. L. Chattin.  It may not be reproduced, posted or distributed without permission of Arizona State University and L. Chattin  In the space below and using proper notation, show the pmf of the random variable corresponding to this MGF.  Use proper notation. Partial credit possible.  

The number of defects in home theater curtain fabric has the Poisson pmf with a mean of 0.040 defects in 1 square foot of fabric. Each home theater curtain contains [t] square feet of fabric.  This copywritten question is part of a quiz or exam at Arizona State.  It may not be posted or reproduced without the permission of the author, Dr. L. Chattin, and Arizona State University.  If we inspect [n] of these curtains and assume they are independent, what is the probability that all of them have no defects?  Express your answer to four decimal places.

Still considering the problem where for a given company the cost function is given by   thousand dollars where x is in thousands of units produced.    Using the results from the previous problem it can be shown that the number of units required to minimize costs is [1].  At that value the minimum cost is [2].  Since it is the minimum, if using the second derivative test, the value of the second derivative at the point would most likely be [3].   This is a partial credit problem.  Clearly label and show the work for your choices for this problem out on the paper used for submission.  The work is to be included in the handwritten support work you are creating for this exam and is to be your own work.  It is required to be part of the submitted file uploaded within 10 minutes after completion of the exam.