Question

Four cutting machines are selected from a large lot of damaged
machines. Each machine is inspected and classified as containing
either a major or a minor defect. Let the random variables X and Y
denote the number of machines with major and minor defects,
respectively. Determine the range of the joint probability
distribution of X and Y.

a.

X >= 0, Y >= 0 and X + Y = 5

b.

X >= 0, Y >= 0 and X + Y = 4

c.

X >= 1, Y >= 1 and X + Y = 5

d.

X >= 1, Y >= 1 and X + Y = 4

Answer #1

Two balls are drawn in succession without replacement from a bag
containing
2 red balls, 1 green balls and 3 green balls. Let X and Y denote
the number
of red and green balls respectively. Find
a) f(x,y) the expression for the joint p.d.f of X and Y [5
Marks]
b) f(x) the expression for the marginal pdf of X [5 Marks]
c) f(y) the expression for the marginal pdf of Y [5 Marks]
d) f(y/x), the expression for the...

Based on the number of voids, a ferrite slab is classied as
either high, medium, or low. Historically, 5% of the slabs are
classied as high, 90% as medium, and 5% as low. A sample of 20
slabs is selected for testing. Let X; Y; and Z denote the number of
slabs that are independently classied as high, medium, and low,
respectively
a. What is the joint probability distribution of X; Y; and Z and
what are it's parameteres (n,p1...)?...

Consider a small ferry that can accommodate cars and buses. The
toll for cars is $3, and the toll for buses is $10. Let X
and Y denote the number of cars and buses, respectively,
carried on a single trip. Suppose the joint distribution of
X and Y is as given in the table below.
y
p(x,y)
0
1
2
x
0
0.025
0.015
0.010
1
0.050
0.030
0.020
2
0.110
0.075
0.050
3
0.150
0.090
0.060
4
0.100
0.060...

Consider a small ferry that can accommodate cars and buses. The
toll for cars is $3, and the toll for buses is $10. Let X
and Y denote the number of cars and buses, respectively,
carried on a single trip. Suppose the joint distribution of
X and Y is as given in the table below.
y
p(x,y)
0
1
2
x
0
0.025
0.015
0.010
1
0.050
0.030
0.020
2
0.050
0.075
0.050
3
0.150
0.090
0.060
4
0.100
0.060...

Consider a small ferry that can accommodate cars and buses. The
toll for cars is $3, and the toll for buses is $10. Let X
and Y denote the number of cars and buses, respectively,
carried on a single trip. Suppose the joint distribution of
X and Y is as given in the table below.
y
p(x,y)
0
1
2
x
0
0.025
0.015
0.010
1
0.050
0.030
0.020
2
0.085
0.075
0.050
3
0.150
0.090
0.060
4
0.100
0.060...

Consider a small ferry that can accommodate cars and buses. The
toll for cars is $3, and the toll for buses is $10. Let X
and Y denote the number of cars and buses, respectively,
carried on a single trip. Suppose the joint distribution of
X and Y is as given in the table below.
y
p(x,y)
0
1
2
x
0
0.025
0.015
0.010
1
0.050
0.030
0.020
2
0.105
0.075
0.050
3
0.150
0.090...

Consider a small ferry that can accommodate cars and buses. The
toll for cars is $3, and the toll for buses is $10. Let X
and Y denote the number of cars and buses, respectively,
carried on a single trip. Suppose the joint distribution of
X and Y is as given in the table below.
y
p(x,y)
0
1
2
x
0
0.025
0.015
0.010
1
0.050
0.030
0.020
2
0.105
0.075
0.050
3
0.150
0.090...

Consider a small ferry that can accommodate cars and buses. The
toll for cars is $3, and the toll for buses is $10. Let X
and Y denote the number of cars and buses, respectively,
carried on a single trip. Suppose the joint distribution of
X and Y is as given in the table below.
y
p(x,y)
0
1
2
x
0
0.025
0.015
0.010
1
0.050
0.030
0.020
2
0.125
0.075
0.050
3
0.150
0.090
0.060
4
0.100
0.060...

Question 1)
A random sample of 15 items is selected from a lot in which the
proportion of defective items is 10%. Find the probability that the
number of defective items in the sample is less than or equal to
3.
A.
Let X be the cost per gallon of gas at a pump, and
X is normally distributed with mean 2.3 and standard
deviation 0.2. If you fill up at a random gas pump, what is the
probability that...

Suppose you will draw 3 marbles without replacement from each of
four bags. Bag 1 has 3 red marbles and 6 black marbles; bag 2 has
10 red marbles and 20 black marbles; bag 3 has 500 red marbles and
1000 black marbles; and bag 4 has an infinite number of marbles,
but twice as many black marbles as red. Let X1, X2, and X3 be the
numbers of red marbles drawn from bag 1, bag 2, and bag 3,...

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