Question 2.3: A product has a maximum life of 100 hours, and its pdf is gi......
A product has a maximum life of 100 hours, and its pdf is given by a triangular distribution, as shown in the figure below. Develop the pdf, cdf, and the reliability function for this product.
Step-by-Step
Its pdf, cdf, and reliability function, respectively, are given below:
f(t)= \begin{cases}\frac{t}{5,000}, & \text { for } 0 \leq t \leq 100 \\ 0, & \text { otherwise }\end{cases}F(t)=\int_0^t f(\tau) d \tau=\int_0^t \frac{\tau}{5,000} d \tau= \begin{cases}0, & \text { for } t<0 \\ \frac{t^2}{10,000}, & \text { for } 0 \leq t \leq 100 \\ 1, & \text { for } t>100\end{cases}
R(t)=1-F(t)= \begin{cases}1, & \text { for } t<0 \\ 1-\frac{t^2}{10,000}, & \text { for } 0 \leq t \leq 100 \\ 0, & \text { for } t>100\end{cases}
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