GATE EE 2014 Set 3 — Question 14
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Question
Lifetime of an electric bulb is a random variable with density , where is measured in years. If the minimum and maximum lifetimes of bulb are 1 and 2 years respectively, then the value of is ________.
Correct answer
0.4 to 0.5
Solution
For a valid probability density function , the total area under the curve must be equal to 1:Given the density function for the interval and otherwise, we integrate over the given range:The value of is approximately , which falls within the range .
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