Question

The life length y (in years) of a memory chip in a laptop computer is a weibull random variable with probability density

f(y)=1/8ye⁻ʸ²/¹⁶ if ≤ y ≤ [infinity]
0 elsewhere
What are the values of α and β?

Answer 1

The Weibull distribution parameters for the given probability density function of the life length of a memory chip in a laptop are α (alpha) = 2 and β (beta) = 4.

Step-by-step explanation:

The question asks about the Weibull distribution parameters for the probability density function (pdf) of the life length of a memory chip in a laptop. The Weibull distribution has two parameters, α (alpha) and β (beta), where α is the shape parameter and β is the scale parameter.

The provided Weibull pdf is f(y) = ⅛ y e^{-y^2/¹⁶} for y ≥ 0 and 0 elsewhere. The general form of the Weibull pdf is f(y) = (α/β) (· (y/β)^(α - 1)) e^{-(y/β)^α}, for y ≥ 0. By comparing the provided pdf to the general form, we can deduce that α = 2 and β = 4. This is because the pdf can be rewritten as f(y) = ⅛ e^{-y^2/16}, which after matching the exponents, indicates a square relationship in the exponent of e, and hence an alpha of 2, and the denominator inside the exponent indicates a β value of 4.