Question

Let f(x) be the probability density function for the lifetime of a manufacturer's highest quality car tire, where x is measured in miles. Explain the meaning of each integral. (a) 50,000 f(x) dx 20,000

Answer 1

P(20000<x<50000)

Explanation:

Given that f(x) is a probability density function for the lifetime of a manufacturer's highest quality car tire, where x is measured in miles.

We have to explain the meaning of integral

20000 to 50000 f(x) dx

=
`\int\limits^(50000)_(20000) }f(x) dx \\=F(50000)-F(20000)`

where F is the cumulative function.

Hence the integral is the probability that x lies between 20000 and 50000

Hence the integral is nothing but

`P(20000<x<50000)`