Question

The probability density function of the time to failure of an electronic component in a copier (in hours) is f(x) e^-x/1074 /1074

Answer 1

Can u add the picture please?? If u don’t mind

Answer 2

The probability density function of the time to failure of an electronic component in a copier (in hours) is $\rm P(a < x < b) =e^\frac{-b}{1074}-e^\frac{-a}{1074}$.

What is the probability density function?

Probability Density Function is a function defining the probability of an outcome for a discrete random variable and is mathematically defined as the derivative of the distribution function.

The given function is;

$\rm =\dfrac{ e^\frac{-x}{1074}}{1074}$

The probability density function of the time to failure of an electronic component in a copier (in hours) is given by;

$\rm P(a < x < b) =\int\limits^a_b {p(x)} \, dx$

For the electronic component, the probability will be:

$\rm P(a < x < b) =\int\limits^a_b {\rm \dfrac{ e^\frac{-x}{1074}}{1074}} \, dx\\\\ P(a < x < b) =\int\limits^a_b {\rm \dfrac{1074}{1074} e^\frac{-x}{1074}}} \, dx\\\\P(a < x < b) =e^\frac{-b}{1074}-e^\frac{-a}{1074}$

Hence, the probability density function of the time to failure of an electronic component in a copier (in hours) is $\rm P(a < x < b) =e^\frac{-b}{1074}-e^\frac{-a}{1074}$.

Learn more about probability here;

https://brainly.com/question/18162805

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