show that negative binomial distribution with the following pdf belongs to the exponential family 2. The Negative Binomial distribution:f(y;0)= ( ³ + ² = ¹ ) 0¹ (1 - 0) ³.y+r-1r-1

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Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.1: Continuous Probability Models

Problem 1YT: Repeat Example 1a for the function f(x)=2x2 on [1,2]. What is the probability that X will be between...

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show that negative binomial distribution with the following pdf belongs to the exponential family

2. The Negative Binomial distribution:
f(y;0)
= ( ³ + ² = ¹ ) 0¹ (1 - 0) ³.
y+r-1
r-1

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

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