Math Help Please?

[匿名]

2018-07-26 9:33 am

The lifetime of a tire selected randomly from a used tire shop is 10,000•X miles, where X is a random variable with the probability density function
f(x)= {6/(x^2) if 2 < x < 3, 0 otherwise

A) What's the probability that a randomly selected tire at this shop lasts fewer than 25,000 miles?

B) Suppose that a randomly selected tire at this shop lasts fewer than 25,000 miles. What's the probability that this tire lasts between 22,500 and 25,000 miles?

更新1:

For A) I got: 0.6 P(10,000X < 25,000) => P(X < 25,000/10,000) => P(X < 2.5) P(X < 2.5) = ∫ [2.5 to 2] [6/(x^2)] dx => -2.4-(-3) => 0.6 Please help me with B, thank you soooooo much! :)

回答 (1)

2018-07-26 9:52 am

✔ 最佳答案

A) We want P(X < 25000/10000)
= P(X < 2.5)
= ∫(x = 2 to 2.5) (6/x^2) dx
= ∫(x = 2 to 2.5) 6x^(-2) dx
= -6x^(-1) {for x = 2 to 2.5}
= 3/5.

B) We want P(22500/10000 < X < 25000/10000)
= P(2.25 < X < 2.5)
= ∫(x = 2.25 to 2.5) (6/x^2) dx
= ∫(x = 2.25 to 2.5) 6x^(-2) dx
= -6x^(-1) {for x = 2.25 to 2.5}
= 4/15.

I hope this helps!

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