Question

Question: Suppose that the battery failure time, measured in hours, has a probability density function, given by f(x) = { 2 / (x + 1)^3 for x >= 0 0 elsewhere - Develop distributions function of x? - Find the probabilities of P(5 <= x <= 10), p(x > 30)?

          Question:

Suppose that the battery failure time, measured in hours, has a probability density function, given by

f(x) = { 2 / (x + 1)^3 for x >= 0
0 elsewhere

- Develop distributions function of x?
- Find the probabilities of P(5 <= x <= 10), p(x > 30)?

Question:

Suppose that the battery failure time, measured in hours, has a probability density function, given by

f(x) = 2 / (x + 1)^3 for x >= 0
0 elsewhere

- Develop distributions function of x?
- Find the probabilities of P(5 <= x <= 10), p(x > 30)?

Added by Cassandra B.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

09/18/2023

Step 1

Since f(x) is defined as 2/(x+1)^3 for x > 0 and 0 elsewhere, we can write the CDF as: F(x) = ∫f(x)dx = ∫(2/(x+1)^3)dx for x > 0 Now, we need to find the integral of 2/(x+1)^3 with respect to x: F(x) = -1/(x+1)^2 + C for x > 0 To find the constant C, we can Show more…

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Suppose that the battery failure time, measured in hours, has a probability density function, given by f(x) = { 2 / (x + 1)^3 for x >= 0 0 elsewhere - Develop distributions function of x? - Find the probabilities of P(5 <= x <= 10), p(x > 30)?