9. (two parts) Induction and complexity: (a) prove that the following propositional function P(n) which asserts that S(n) (the arithmetic series) holds for all non-zero natural numbers n e N*: Three steps are required: (a) first show the basis case and then (b) show that P(k) = P(k +1) is true; (c) prove and then |claim the final result is true by the inductive hypothesis: VnP(n). Recall the axiom of induction is, in logical symbols, VP. [[P(0) ^ V(k e N). [P(k) = P(k+1)]] = V(n e N). P(n)] where P is any predicate and k and n are both natural numbers. Number your three steps clearly. n(n + 1) S(n) = 1+2+ 3+ ...+n = 2
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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![9. (two parts) Induction and complexity:
(a) prove that the following propositional function P(n) which asserts that S(n) (the arithmetic series) holds
for all non-zero natural numbers n e N*:
Three steps are required: (a) first show the basis case and then (b) show that P(k) = P(k +1) is true; (c) prove and then
|claim the final result is true by the inductive hypothesis: VnP(n). Recall the axiom of induction is, in logical symbols,
VP. [[P(0) ^ V(k e N). [P(k) = P(k+1)]] = V(n e N). P(n)] where P is any predicate and k and n are both natural
numbers. Number your three steps clearly.
n(n + 1)
S(n) = 1+2+ 3+ ...+n =
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