Find the R Th Term in the Binomial Expansion $$( z + d ) ^ { n }$$

question 29

Multiple Choice

Find the r th term in the binomial expansion. $$( z + d ) ^ { n }$$

• A) \(\frac { n ! } { ( n - r ) ! r ! } z ^ { n - r } d ^ { r }\)
• B) \(\frac { n ! } { ( n + r - 1 ) ! ( r + 1 ) ! } z ^ { n + r - 1 } d ^ { r + 1 }\)
• C) \(\frac { n ! } { ( n - r + 1 ) ! ( r - 1 ) ! } z ^ { n - r } d ^ { r - 1 }\)
• D) \(\quad \frac { n ! } { ( n - r ) ! r ! } z ^ { n - r + 1 } d ^ { r - 1 }\)
• E) \(\frac { n ! } { ( n - r + 1 ) ! ( r - 1 ) ! } z ^ { n - r + 1 } d ^ { r - 1 }\)

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Definitions:

Uniform Distribution

A type of probability distribution where all outcomes are equally likely to occur within a certain range.

Continuous Uniform

A distribution that assigns an equal probability to all outcomes in a continuous range.

Random Variable

A variable whose possible values are outcomes of a statistical experiment, where the value is determined by chance.

Probability Density Function

A function that describes the relative likelihood for a continuous random variable to take on a given value.