Answer:
a) X ~ [tex]e(0.03)[/tex]
b) μ = 100/3
c) [tex] \sigma = 100/3 [/tex]
d) A battery is expected to last 100/3 months (33 months and 10 days approximately).
e) For seven batteries, i would expect them to last 700/3 months (approximately 19 years, 5 months and 10 days).
Step-by-step explanation:
a) The life of a battery is usually modeled with an exponential distribution X ~ [tex]e(0.03)[/tex]
b) The mean of X is μ = 1/0.03 = 100/3
c) The standard deviation is [tex] \sigma = 1/0.03 = 100/3 [/tex]
d) The expected value of the bateery life is equal to its mean, hence it is 100/3 months.
e) The expected value of 7 (independent) batteries is the sum of the expected values of each one, hence it is 7*100/3 = 700/3 months.
