Question

(6) The lifetime T of a car battery (in years) has a PDF given by $f(t) = \begin{cases} 2t & 0 \le t < \frac{1}{2} \\ \frac{3}{4} & \frac{1}{2} \le t < 3 \\ 0 & \text{otherwise} \end{cases}$ APPLIED & CONCEPTUAL PROBLEM SET 2 The battery manufacturer promises to pay out $50 dollars if the battery dies within 2.5 years, and pays out nothing if the battery dies after 2.5 years. What is the expected payout per battery. (Hint: Answer is $31.25)

          (6) The lifetime T of a car battery (in years) has a PDF given by
$f(t) = \begin{cases} 2t & 0 \le t < \frac{1}{2} \\ \frac{3}{4} & \frac{1}{2} \le t < 3 \\ 0 & \text{otherwise} \end{cases}$

APPLIED & CONCEPTUAL PROBLEM SET
2
The battery manufacturer promises to pay out $50 dollars if the battery dies within 2.5 years, and
pays out nothing if the battery dies after 2.5 years. What is the expected payout per battery.
(Hint: Answer is $31.25)

(6) The lifetime T of a car battery (in years) has a PDF given by
f(t) = 2t 0 ≤ t < (1)/(2)
(3)/(4) (1)/(2)≤ t < 3
0 otherwise

APPLIED CONCEPTUAL PROBLEM SET
2
The battery manufacturer promises to pay out 50 dollars if the battery dies within 2.5 years, and
pays out nothing if the battery dies after 2.5 years. What is the expected payout per battery.
(Hint: Answer is31.25)

Added by April C.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Narayan Hari

02/24/2022

Step 1

5 years. To find the probability, we need to integrate the PDF over the interval [0, 2.5]: P(T <= 2.5) = ∫[0,2.5] 2t dt = t^2 |[0,2.5] = (2.5)^2 - (0)^2 = 6.25 Show more…

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(6) Please provide clear steps and explanation (6) The lifetime T of a car battery (in years) has a PDF given by (2t0t< 2<t<3 0 otherwise APPLIED & CONCEPTUAL PROBLEM SET The battery manufacturer promises to pay out $50 dollars if the battery dies within 2.5 years,and pays out nothing if the battery dies after 2.5 years. What is the expected payout per battery. (Hint: Answer is $31.25)