2. In a clinic with two physicians, Dr. X and Dr.
Y, each doctor can be scheduled to see at most 3 patients per hour. The joint probability mass function
is given by the following table.
a.) State two marginal probability mass
functions pX and pY.
b.) If we were to assume that Dr. X
will see 2 patients in a given hour, what is the probability that Dr. Y will
see exactly 1 patient?
c.) If we were to assume that Dr. Y
will see 0 patients in a given hour, what is the probability that Dr. X will
see exactly 1 patient?
d.) Is the number of patients seen in
an hour by Dr. Y independent of the number of patients seen by Dr. X? Prove your answer.
e.) What are the average and standard
deviation in the number of patients seen per hour by Dr. X?
f.) What are the average and standard
deviation in the number of patients seen per hour by Dr. Y?
g.) What is the probability that in any
given hour Dr. X will see more patients than Dr. Y?
Answers:
(Overà)
3. (Given three independent, normally
distributed random variables, X1,
X2, and X3, with means and standard
deviations as follows,mX1 = 4.00, sX1 = 0.40, mX2 = 2.00, sX2 = 0.20, mX3 = 5.00, sX3 = 0.50, you need to study a random variable Ydefined as
Y =
2X1 + 1.5X2
– X3.
a.) What is the mean of random variable
Y?
b.) What is the standard deviation of
random variable Y?
c.) Is Ynormally distributed? Why
or why not?
d.) What is the probability that any
given outcome for Y will be a value
between 4.02 and 7.98?
Answers:
