SOLVED:The lifetime (hours) of an electronic device is a random variable with the following exponential probability density function. f(x)=(1)/(50) e^-x / 50 for x ≥ 0 a. What is the mean lifetime of the device? b. What is the probability that the device will fail in the first 25 hours of operation? c. What is the probability that the device will operate 100 or more hours before failure?

Probability density functions

Consider the following exponential probability density function.a. Which of the following is the formula for P(𝑥 > 𝑥₀)?1. P(𝑥 > 𝑥₀) = 𝑒^(-𝑥₀)2. P(𝑥 > 𝑥₀) = 1 - 𝑒^(-𝑥₀)3. P(𝑥 > 𝑥₀) = 1 - 𝑒^(-𝑧₀)b. Find P(𝑥 > 2) (to 4 decimals).c. Find P(𝑥 > 3) (to 4 decimals).d. Find P(𝑥 > 5) (to 4 decimals).e. Find P(2 < 𝑥 < 5) (to 4 decimals).

Exponential growth & decay word problems

Exponential Growth and Decay (examples, solutions, worksheets, videos, activities)

Exponential Growth and Decay Word Problems