Question

Problem 1 The demand for a certain weekly magazine at a newsstand is a discrete random variable, X, with an expected value of 3 magazines sold per week. Furthermore, the distribution of variable X is symmetric about the value of 3. The magazines are sold for $6.00 per copy to the customers and cost $4.00 per copy for the owner of the newsstand. At the beginning of each week, the owner of the newsstand buys 6 magazines to sell during the week.

(a) The table below is intended to present the distribution of variable X. Complete the table. Justify your values. x (value of X) 0 1 2 3 4 5 6 Probability of x 0.05 0.10 0.20

(b) In dollars, what is the expected amount of money the owner of the newsstand will take in (the gross income minus the expense mentioned above) from the sales of the magazines per week? (show your work) (hint: maybe, first, you want to present a table similar to the one above)

(c) Explain briefly why it is not wise for the owner of the newsstand to buy 6 magazines at the beginning of each week. (longwinded explanations will lower your score)

Answer #1

Weekly demand for the Muscat Star magazine is normally distributed
with a mean of 11.73 and a standard deviation of 4.47. The
magazines are sold for OMR 0.750 and bought for OMR 0.250. The
unsold copies can be salvaged for OMR 0.100.
1. Find the order quantity that minimizes the expected total
cost.
2. What would be the order up-to point if the shop receives 6
copies of the magazine from another supplier at the beginning of
the week?
3....

x
P(X=x)
0
0.44
The incomplete
table at right is a discrete random variable x's
probability distribution, where x is the number of days in
a week people exercise. Answer the following:
1
0.18
2
0.02
3
(a)
Determine the
value that is missing in the table.
4
0.03
5
0.13
6
0.07
(b)
Explain the meaning of " P(x < 2) " as it applies to the context
of this problem.
7
0.04
(c)
Determine the
value of P(x >...

Problem #3. X is a random variable with an exponential
distribution with rate λ = 7 Thus the pdf of X is f(x) = λ
e−λx for 0 ≤ x where λ = 7.
a) Using the f(x) above and the R integrate function calculate the
expected value of X.
b) Using the f(x) above and the R integrate function calculate the
expected value of X2
c) Using the dexp function and the R integrate command calculate
the expected value...

1. Let X be a discrete random variable. If Pr(X<6) = 1/5, and
Pr(X>6) = 1/7, then what is Pr(X=6)?
Please specify your answer in decimal terms and round your
answer to the nearest hundredth (e.g., enter 12 percent as
0.12).
2. A department store manager has monitored the number of
complaints received per week about poor service. The probabilities
for numbers of complaints in a week, established by this review,
are shown in the table.
Number of complaints
0...

2.
The incomplete
probability distribution table at the right is of the discrete
random variable x representing the number of times people
donate blood in 1 year. Answer the following:
x
P(X=x)
(a)
Determine the
value that is missing in the table. (Hint: what are the
requirements for a probability distribution?)
0
0.532
1
0.124
2
0.013
(b)
Find the
probability that x is at least 2 , that is find
P(x ≥ 2).
3
0.055
4
0.129
5
(c)...

Question 1 (General Discrete)
Household Size from U.S. Census of 2010
Let X be the random variable: number of people (persons!) in a
household.
Number of people in household (x)
Probability
P(X=x)
xP(x)
x-μ
x-μ2
P(x)x-μ2
1
0.267
2
0.336
3
0.158
4
0.137
5
0.063
6
0.024
7
0.015
Totals:
Confirm that this is a probability distribution.
Draw a bar chart.
Is the distribution symmetric, left or right skewed?
Calculate the mean and standard deviation.
What is the probability...

1. A coin is tossed 3 times. Let x be the random discrete
variable representing the number of times tails comes up.
a) Create a sample space for the event;
b) Create a probability distribution table for the discrete
variable
x;
c) Calculate the expected value for x.
2. For the data below, representing a sample of times (in
minutes) students spend solving a certain Statistics problem, find
P35, range, Q2 and IQR.
3.0, 3.2, 4.6, 5.2 3.2, 3.5...

Question 6) Suppose X is a random variable taking on possible
values 0,2,4 with respective probabilities .5, .3, and .2. Y is a
random variable independent from X taking on possible values 1,3,5
with respective probabilities .2, .2, and .6. Use R to determine
the following.
f) Find the expected value of X*Y. (i.e. X times Y)
g) Find the expected value of 3X - 5Y.
h) Find the variance of 3X - 5Y
i) Find the expected value of...

Question 1
Refer to the probability function given in the following table
for a
random variable X that takes on the values 1,2,3 and 4
X 1 2 3 4
P(X=x) 0.4 0.3 0.2 0.1
a) Verify that the above table meet the conditions
for being a discrete probability
distribution
b) Find P(X<2)
c) Find P(X=1 and X=2)
d) Graph P(X=x)
e) Calculate the mean of the random variable
X
f) Calculate the standard deviation of the random
variable X...

Part II
Suppose the discrete random variable X has the
following probability distribution.
x
-2
0
2
4
6
P(X=x)
0.09
0.24
0.33
a
0.14
Find the value of a so that
this probability distribution is valid. (Sec. 4.3)
(Sec. 4.4)
Find the mean of the random variable X in Exercise 1
above.
Find the variance of the random variable X in Exercise
1 above.
Consider the following table for the number of automobiles in
Canada in 2005 by vehicle...

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