Math Problem Statement
The lifetime, in years, of some electronic component is a continuous random variable with the density
f(x) =
Find
a) The value of k, as f(x) is valid density function.
b) the cumulative distribution function,
c) the probability for the lifetime to exceed 2 years.
Solution
To help you with the questions, we need to assume that you are dealing with a valid probability density function (pdf) that is defined as . However, the exact form of is missing in your query. A typical pdf is often given in a piecewise format, for example:
\begin{cases} k \cdot g(x) & \text{for } x \in [0, \infty) \\ 0 & \text{otherwise} \end{cases}$$ where $$k$$ is a constant and $$g(x)$$ is some function defining the pdf. In order to proceed, I'll need the specific form of $$f(x)$$ to give accurate solutions. Could you please provide the functional form of $$f(x)$$? Once I have that, I can: - Find the value of $$k$$ using the property that the total probability must sum to 1. - Compute the cumulative distribution function (CDF). - Calculate the probability that the lifetime exceeds 2 years.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Probability
Probability Density Function (PDF)
Cumulative Distribution Function (CDF)
Integrals
Formulas
f(x) = k * g(x) for x in [0, ∞)
∫_0^∞ f(x) dx = 1 (Normalization Condition)
CDF: F(x) = ∫_0^x f(t) dt
Theorems
Normalization Condition for PDFs
Definition of CDF
Suitable Grade Level
College (Undergraduate)
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