In Problems, 63 - 68 , a sample space S is described. Would it be reasonable to make the equally likely assumption? Explain. A wheel of fortune has seven sectors of equal area colored red, orange, yellow, green, blue, indigo, and violet. We are interested in the color that the pointer indicates when the wheel stops, so an appropriate sample space is S = R , O , Y , G , B , I , V .
In Problems, 63 - 68 , a sample space S is described. Would it be reasonable to make the equally likely assumption? Explain. A wheel of fortune has seven sectors of equal area colored red, orange, yellow, green, blue, indigo, and violet. We are interested in the color that the pointer indicates when the wheel stops, so an appropriate sample space is S = R , O , Y , G , B , I , V .
In Problems,
63
-
68
, a sample space
S
is described. Would it be reasonable to make the equally likely assumption? Explain.
A wheel of fortune has seven sectors of equal area colored red, orange, yellow, green, blue, indigo, and violet. We are interested in the color that the pointer indicates when the wheel stops, so an appropriate sample space is
S
=
R
,
O
,
Y
,
G
,
B
,
I
,
V
.
Definition Definition For any random event or experiment, the set that is formed with all the possible outcomes is called a sample space. When any random event takes place that has multiple outcomes, the possible outcomes are grouped together in a set. The sample space can be anything, from a set of vectors to real numbers.
Example 1 Solve the heat equation initial-boundary-value problem
U₁ =3xx
(2,0)=2(x-2),
u(0,t) = u(x, t)=0.
4.96 The breaking strengths for 1-foot-square samples of a particular synthetic fabric are approximately normally distributed with a mean of 2,250 pounds per square inch (psi) and a standard deviation of 10.2 psi. Find the probability of selecting a 1-foot-square sample of material at random that on testing would have a breaking strength in excess of 2,265 psi.4.97 Refer to Exercise 4.96. Suppose that a new synthetic fabric has been developed that may have a different mean breaking strength. A random sample of 15 1-foot sections is obtained, and each section is tested for breaking strength. If we assume that the population standard deviation for the new fabric is identical to that for the old fabric, describe the sampling distribution forybased on random samples of 15 1-foot sections of new fabric
Each of the following statements is an attempt to show that a given series is convergent or
divergent using the Comparison Test (NOT the Limit Comparison Test.) For each statement, enter C
(for "correct") if the argument is valid, or enter | (for "incorrect") if any part of the argument is
flawed. (Note: if the conclusion is true but the argument that led to it was wrong, you must enter I.)
☐ 1. For all n > 1,
seriesΣ In(n)
In(n)
converges.
2, 1,
arctan(n)
the series arctan(n)
n³
☐ 4. For all n > 1,
123
converges.
1
n ln(n)
series In(n) diverges.
2n
.
and the seriesΣconverges, so by the Comparison Test,
2, 3, and the series converges, so by the Comparison Test, the
series-3
1
converges.
☐ 6. For all n > 2, In(n) >, and the series Σ converges, so by the Comparison Test, the
seriesΣ
In(n) converges.
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Probability & Statistics (28 of 62) Basic Definitions and Symbols Summarized; Author: Michel van Biezen;https://www.youtube.com/watch?v=21V9WBJLAL8;License: Standard YouTube License, CC-BY
Introduction to Probability, Basic Overview - Sample Space, & Tree Diagrams; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=SkidyDQuupA;License: Standard YouTube License, CC-BY