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 + ...
T1.4: Let ẞ(G) be the minimum size of a vertex cover, a(G) be the maximum size of an
independent set and m(G) = |E(G)|.
(i) Prove that if G is triangle free (no induced K3) then m(G) ≤ a(G)B(G). Hints - The
neighborhood of a vertex in a triangle free graph must be independent; all edges have at least
one end in a vertex cover.
(ii) Show that all graphs of order n ≥ 3 and size m> [n2/4] contain a triangle. Hints - you
may need to use either elementary calculus or the arithmetic-geometric mean inequality.
We consider the one-period model studied in class as an example. Namely, we assumethat the current stock price is S0 = 10. At time T, the stock has either moved up toSt = 12 (with probability p = 0.6) or down towards St = 8 (with probability 1−p = 0.4).We consider a call option on this stock with maturity T and strike price K = 10. Theinterest rate on the money market is zero.As in class, we assume that you, as a customer, are willing to buy the call option on100 shares of stock for $120. The investor, who sold you the option, can adopt one of thefollowing strategies: Strategy 1: (seen in class) Buy 50 shares of stock and borrow $380. Strategy 2: Buy 55 shares of stock and borrow $430. Strategy 3: Buy 60 shares of stock and borrow $480. Strategy 4: Buy 40 shares of stock and borrow $280.(a) For each of strategies 2-4, describe the value of the investor’s portfolio at time 0,and at time T for each possible movement of the stock.(b) For each of strategies 2-4, does the investor have…
Negate the following compound statement using De Morgans's laws.
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