Final answer:
To determine E(eZ+99), where Z is a standard normal random variable, use the properties of the normal distribution and integrate the random variable times the probability density function over its entire range.
Step-by-step explanation:
To determine E(eZ+99), where Z is a standard normal random variable, we need to use properties of the normal distribution. Since Z is a standard normal random variable, its mean, denoted as μ, is 0, and its standard deviation, denoted as σ, is 1. In this case, we want to find the expected value of eZ+99.
The expected value of a random variable can be found by integrating the random variable times the probability density function (pdf) over its entire range. For a standard normal random variable, the pdf is given by f(z) = (1/√2π) * e^(-z^2/2).
For eZ+99, the expected value is:
E(eZ+99) = ∫ (e^(z+99)) * (1/√2π) * e^(-z^2/2) dz
Simplifying and evaluating this integral will give you the answer.