X observes a Weibull distribution with shape parameterβ = 5and characteristic lifeη = 45Find the mean of X (answers to 2 decimal places)

The mean of a Weibull distribution is given by the formula:

Mean = η * Γ(1 + 1/β)

where Γ is the gamma function, η is the scale parameter (characteristic life), and β is the shape parameter.

Given that η = 45 and β = 5, we can substitute these values into the formula:

Mean = 45 * Γ(1 + 1/5)

The gamma function Γ(1 + 1/5) can be calculated using a scientific calculator or a software package like R or Python. The value is approximately 1.03.

So, the mean of X is approximately:

Mean = 45 * 1.03 = 46.35

So, the mean of X is approximately 46.35 (rounded to two decimal places).