A single card is drawn from a standard 52 -card deck. Let D be the event that the card drawn is a diamond, and let F be the event that the card drawn is a face card. In Problems 13 - 24 , find the indicated probabilities. P D ∪ F
A single card is drawn from a standard 52 -card deck. Let D be the event that the card drawn is a diamond, and let F be the event that the card drawn is a face card. In Problems 13 - 24 , find the indicated probabilities. P D ∪ F
Solution Summary: The author calculates the probability P(Dcup F), if a card is taken out from the deck of 52 -cards.
A single card is drawn from a standard
52
-card
deck. Let
D
be the event that the card drawn is a diamond, and let
F
be the event that the card drawn is a face card. In Problems
13
-
24
, find the indicated probabilities.
Write a Regression summary explaining significance of mode, explaining regression coefficients, significance of the independent variables, R and R square.
Premiums earned
Net income
Dividends
Underwriting Gain/ Loss
30.2
1.6
0.6
0.1
47.2
0.6
0.7
-3.6
92.8
8.4
1.8
-1.5
95.4
7.6
2
-4
100.4
6.3
2.2
-8.1
104.9
6.3
2.4
-10.8
113.2
2.2
2.3
-18.2
130.3
3.0
2.4
-21.4
161.9
13.5
2.3
-12.8
182.5
14.9
2.9
-5.9
193.3
11.7
2.9
-7.6
1. Show that the vector field
F(x, y, z)
=
(2x sin ye³)ix² cos yj + (3xe³ +5)k
satisfies the necessary conditions for a conservative vector field, and find a potential function for
F.
1. Newton's Law of Gravitation (an example of an inverse square law) states that the magnitude
of the gravitational force between two objects with masses m and M is
|F|
mMG
|r|2
where r is the distance between the objects, and G is the gravitational constant. Assume that the
object with mass M is located at the origin in R³. Then, the gravitational force field acting on
the object at the point r = (x, y, z) is given by
F(x, y, z) =
mMG
r3
r.
mMG
mMG
Show that the scalar vector field f(x, y, z) =
=
is a potential function for
r
√√x² + y² .
Fi.e. show that F = Vf.
Remark: f is the negative of the physical potential energy, because F = -V(-ƒ).
Chapter 8 Solutions
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Elementary Statistics: Picturing the World (7th Edition)
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