# The lifetime, in hundreds of hours, of a light bulb is a continuous random variable with density

## Question:

The lifetime, in hundreds of hours, of a light bulb is a continuous random variable with density function f (x) = ????2xe−????x, x > 0, where ???? > 0.

(i) Calculate the distribution function of X.

(ii) What is the expected value and the variance for the lifetime of a bulb?

(iii) From past data, it has been estimated that the average length of lifetime for a bulb of this type is 2500 hours. Which value of ???? should be used to describe the distribution of bulb lifetimes? Using this value of ????, calculate the probability that a randomly selected light bulb will last for more than 2500 hours.

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**Related Book For**

## Introduction To Probability Volume 2

**ISBN:** 9781118123331

1st Edition

**Authors:** Narayanaswamy Balakrishnan, Markos V. Koutras, Konstadinos G. Politis