Visualize that two tributaries A and B at their confluence form a river C. Statistical properties of flow data for tributaries A and B indicate that tributary A has a yearly discharge rate smaller than its mean flow rate (?̅?) in 50% of the years while tributary B has a yearly discharge rate smaller than its mean flow rate (?̅?) in 60% of the time. In 70% of the years in which tributary A has a discharge rate smaller than its mean discharge rate (?̅?), tributary B also has a discharge rate smaller than its mean discharge rate (?̅?). Compute the probability that (i) both tributaries have a discharge rate smaller than their mean discharge rates, (ii) at least one tributary has a discharge rate smaller than its mean discharge rate, (iii) tributary A has a discharge rate smaller than its mean discharge rate given that tributary B has a discharge rate smaller than its mean discharge rate, (iv) at least one tributary has discharge rate higher than its mean discharge rate, and (v) probability of no shortage of discharge rate in River C if no shortage of discharge rate occurs when both tributaries (A and B) have discharge rates higher than their respective mean discharge rates.
Visualize that two tributaries A and B at their confluence form a river C. Statistical properties of flow data for tributaries A and B indicate that tributary A has a yearly discharge rate smaller than its mean flow rate (?̅?) in 50% of the years while tributary B has a yearly discharge rate smaller than its mean flow rate (?̅?) in 60% of the time. In 70% of the years in which tributary A has a discharge rate smaller than its mean discharge rate (?̅?), tributary B also has a discharge rate smaller than its mean discharge rate (?̅?). Compute the probability that (i) both tributaries have a discharge rate smaller than their mean discharge rates, (ii) at least one tributary has a discharge rate smaller than its mean discharge rate, (iii) tributary A has a discharge rate smaller than its mean discharge rate given that tributary B has a discharge rate smaller than its mean discharge rate, (iv) at least one tributary has discharge rate higher than its mean discharge rate, and (v) probability of no shortage of discharge rate in River C if no shortage of discharge rate occurs when both tributaries (A and B) have discharge rates higher than their respective mean discharge rates.
Visualize that two tributaries A and B at their confluence form a river C. Statistical properties of flow data for tributaries A and B indicate that tributary A has a yearly discharge rate smaller than its mean flow rate (?̅?) in 50% of the years while tributary B has a yearly discharge rate smaller than its mean flow rate (?̅?) in 60% of the time. In 70% of the years in which tributary A has a discharge rate smaller than its mean discharge rate (?̅?), tributary B also has a discharge rate smaller than its mean discharge rate (?̅?). Compute the probability that (i) both tributaries have a discharge rate smaller than their mean discharge rates, (ii) at least one tributary has a discharge rate smaller than its mean discharge rate, (iii) tributary A has a discharge rate smaller than its mean discharge rate given that tributary B has a discharge rate smaller than its mean discharge rate, (iv) at least one tributary has discharge rate higher than its mean discharge rate, and (v) probability of no shortage of discharge rate in River C if no shortage of discharge rate occurs when both tributaries (A and B) have discharge rates higher than their respective mean discharge rates.
Visualize that two tributaries A and B at their confluence form a river C. Statistical properties of flow data for tributaries A and B indicate that tributary A has a yearly discharge rate smaller than its mean flow rate (?̅?) in 50% of the years while tributary B has a yearly discharge rate smaller than its mean flow rate (?̅?) in 60% of the time. In 70% of the years in which tributary A has a discharge rate smaller than its mean discharge rate (?̅?), tributary B also has a discharge rate smaller than its mean discharge rate (?̅?). Compute the probability that (i) both tributaries have a discharge rate smaller than their mean discharge rates, (ii) at least one tributary has a discharge rate smaller than its mean discharge rate, (iii) tributary A has a discharge rate smaller than its mean discharge rate given that tributary B has a discharge rate smaller than its mean discharge rate, (iv) at least one tributary has discharge rate higher than its mean discharge rate, and (v) probability of no shortage of discharge rate in River C if no shortage of discharge rate occurs when both tributaries (A and B) have discharge rates higher than their respective mean discharge rates.
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 + ...
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