Question

Find the indicated probability, given that the lifetime of a lightbulb is exponentially distributed with pdf f(x) = 6e^-6x (with x measured in years). The lightbulb lasts less than 3 months.

Answer 1

What class is this for?

Answer 2

calculus

Answer 3

@rizwan_uet can u help?

Answer 4

i m very weak at probability sorrr @onegirl

Answer 5

*sorry

Answer 6

ok

Answer 7

@cwrw238 can u help?

Answer 8

convert 3 months to years and integrate

Answer 9

\[P(X<a)=P(0\le X<a)=\int\limits_{0}^{a}6e^{-6x}dx\]

Answer 10

where \(a\) is in years

Answer 11

so i get 0.25 so whats next?

Answer 12

so i will substitute 0.25 into a and solve.

Answer 13

yes

Answer 14

okay thanks