If X1, X2, and X3 are independent and have the means4, 9, and 3 and the variances 3, 7, and 5, find the mean andthe variance of(a) Y = 2X1 − 3X2 + 4X3;(b) Z = X1 + 2X2 − X3.
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.
If X1, X2, and X3 are independent and have the means
4, 9, and 3 and the variances 3, 7, and 5, find the mean and
the variance of(a) Y = 2X1 − 3X2 + 4X3;
(b) Z = X1 + 2X2 − X3.
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