(a) Let f(x) = px² + 2qx + r with p > 0. By considering the minimum, prove that f(x) > 0 for all real x if and only if q² – pr < 0. - (b) Let a (dot product) of these two vectors are defined as (a1, a2, .. an) and b = (b1, b2, ..., bn) be any two vectors in R". The inner product ... a -5 = a,b1 + azb2 + + anbn, .. and also the norms of these vectors are defined as ||| V až + až + + a유, |||| = V5 . 5 = /bỉ + b3 + + b유. = Vā a
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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