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

Answer:

P(20000<x<50000)

Step-by-step 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

$P(20000$