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10 Generalized Linear Regression In the problems of this section $x^T \beta = \beta_0 + \sum_{i=1}^p \beta_i x_i$ Problem 10.5. Y is an exponentially distributed random variable with parameter $\lambda > 0$, we write Y ~ Exp($\lambda$), if its probability density function is $f(y; \lambda) = \begin{cases} \lambda e^{-\lambda y} & y \ge 0, \\ 0 & y < 0. \end{cases}$ $\lambda$ is sometimes called the rate parameter. We want to construct a generalized linear model (exponential regression). We know that E[Y] = 1/$\lambda$, this need not be derived here. a) Find the canonical link function relating $x^T \beta$ to the mean. What does this require from $x^T \beta$? b) Write down the probability density function $f(y; x^T \beta)$. c) What is E[Y|x] in exponential regression?

          10 Generalized Linear Regression
In the problems of this section
$x^T \beta = \beta_0 + \sum_{i=1}^p \beta_i x_i$
Problem 10.5.
Y is an exponentially distributed random variable with parameter $\lambda > 0$, we write Y ~
Exp($\lambda$), if its probability density function is
$f(y; \lambda) = \begin{cases} \lambda e^{-\lambda y} & y \ge 0, \\ 0 & y < 0. \end{cases}$
$\lambda$ is sometimes called the rate parameter. We want to construct a generalized linear model
(exponential regression). We know that E[Y] = 1/$\lambda$, this need not be derived here.
a) Find the canonical link function relating $x^T \beta$ to the mean. What does this require from
$x^T \beta$?
b) Write down the probability density function
$f(y; x^T \beta)$.
c) What is E[Y|x] in exponential regression?

10 Generalized Linear Regression
In the problems of this section
x^T β = β0 + ∑i=1^p xi
Problem 10.5.
Y is an exponentially distributed random variable with parameter λ > 0, we write Y
Exp(λ), if its probability density function is
f(y; λ) = λ e^-λ y y ≥ 0,
0 y < 0.
λ is sometimes called the rate parameter. We want to construct a generalized linear model
(exponential regression). We know that E[Y] = 1/λ, this need not be derived here.
a) Find the canonical link function relating x^T β to the mean. What does this require from
x^T β?
b) Write down the probability density function
f(y; x^T β).
c) What is E[Y|x] in exponential regression?

Added by Glenn Z.

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