Random variable, X, has the MGF :   MX(t) = 0.21 + 0.30et  +  0.20e3t + 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.

A psychology experiment asked 20 people to choose a number: 1, 2, 3, or 4.  The experimenter believed that these numbers would be chosen according to a discrete uniform distribution. 6 people chose the number 1 3 people chose the number 2 8 people chose the number 3 3 people chose the number 4 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. Perform a Chi-Square Goodness of Fit test on this data.  The p-value for this test is ___________.  Enter your answer to 3 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. 

An ASU student is taking two summer courses: MAT 275 and IEE 385.  The grades that the student will receive are assumed to be independent.  The probability that the student gets a C or better in MAT 275 is 0.75 and the probability that the student gets a C or better in IEE 385 is 0.78.  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.  X is the number of summer courses in which the student gets a C or better. F(0) = , F(1) = , F(2) = , F(3.5) = .  Choose the answers closest to yours. 

Below is the moment generating function for random variable, X: MX(t) = (2/6)et + (1/2)e2t 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.  V(X) = _______. Answer to four decimal places.

On a product line that you manage, the number of inspections until the first failure each day is thought to have the geometric pmf.  For one 6-day week, you collect data: On Monday the first failure occurred on inspection #. On Tuesday the first failure occurred on inspection #. On Wednesday the first failure occurred on inspection #. On Thursday the first failure occurred on inspection #. On Friday the first failure occurred on inspection #. On Saturday the first failure occurred on inspection #.  This copywritten question is part of a quiz or exam given at Arizona State University. It may not be posted or reproduced without permission from Dr. L. Chattin.  Determine the maximum likelihood estimate of the parameter, p, to three decimal places.  (Remember, if a number has trailing 0s, such as 0.030, Canvas will edit your entry to 0.03.)

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 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 am on consecutive days (Monday through Friday).  Assume independence. 

For a given company the cost function is given by   thousand dollars where x is in thousands of units produced.    Put the steps in order to determine the minimum cost.