Roller Coasters The table shows the names and heights of some of the tallest roller coasters in the United States. (Source: Today.com) a. Find and interpret (report in context) the mean height of these roller coasters. b. Find and interpret the standard deviation of the height of these roller coasters. c. If the Kingda Ka coaster was only 420 feet high, how would this affect the mean and standard deviation you calculated in (a) and (b). Now recalculate the mean and standard deviation using 420 as the height of Kingda Ka. Was your prediction correct?
Roller Coasters The table shows the names and heights of some of the tallest roller coasters in the United States. (Source: Today.com) a. Find and interpret (report in context) the mean height of these roller coasters. b. Find and interpret the standard deviation of the height of these roller coasters. c. If the Kingda Ka coaster was only 420 feet high, how would this affect the mean and standard deviation you calculated in (a) and (b). Now recalculate the mean and standard deviation using 420 as the height of Kingda Ka. Was your prediction correct?
Roller Coasters The table shows the names and heights of some of the tallest roller coasters in the United States. (Source: Today.com)
a. Find and interpret (report in context) the mean height of these roller coasters.
b. Find and interpret the standard deviation of the height of these roller coasters.
c. If the Kingda Ka coaster was only 420 feet high, how would this affect the mean and standard deviation you calculated in (a) and (b). Now recalculate the mean and standard deviation using 420 as the height of Kingda Ka. Was your prediction correct?
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
Throughout, A, B, (An, n≥ 1), and (Bn, n≥ 1) are subsets of 2.
1. Show that
AAB (ANB) U (BA) = (AUB) (AB),
Α' Δ Β = Α Δ Β,
{A₁ U A2} A {B₁ U B2) C (A1 A B₁}U{A2 A B2).
16. Show that, if X and Y are independent random variables, such that E|X|< ∞,
and B is an arbitrary Borel set, then
EXI{Y B} = EX P(YE B).
Proposition 1.1 Suppose that X1, X2,... are random variables. The following
quantities are random variables:
(a) max{X1, X2) and min(X1, X2);
(b) sup, Xn and inf, Xn;
(c) lim sup∞ X
and lim inf∞ Xn-
(d) If Xn(w) converges for (almost) every w as n→ ∞, then lim-
random variable.
→ Xn is a
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