The shelf life (in years) of a laser pointer battery is a continuous random variable with probability density function f ( x ) = { 1 / ( x + 1 ) 2 i f x ≥ 0 0 otherwise (A) Find the probability that a randomly selected laser pointer battery has a shelf life of 3 years or less. (B) Find the probability that a randomly selected laser pointer battery has a shelf life of from 3 to 9 years. (C) Graph y = f ( x ) for [0, 10] and show the shaded region for part (A).
The shelf life (in years) of a laser pointer battery is a continuous random variable with probability density function f ( x ) = { 1 / ( x + 1 ) 2 i f x ≥ 0 0 otherwise (A) Find the probability that a randomly selected laser pointer battery has a shelf life of 3 years or less. (B) Find the probability that a randomly selected laser pointer battery has a shelf life of from 3 to 9 years. (C) Graph y = f ( x ) for [0, 10] and show the shaded region for part (A).
Solution Summary: The author explains that the probability of a randomly selected laser pointer battery having 3 years or less is 0.75.
A random variable X has the probability density function as
f(x) = Ax(9-X2) 0 ≤ x ≤ 3
= 0 otherwise
Find the value of A, the mean and the standard deviation of X.
The lifetime X in hours of an electronic tube is a random variable
having a probability density function given by
f(r) = re, I
(a) Compute the expected lifetime of such a tube.
(b) Compute the variance of the lifetime of such a tube.
(c) Find the median lifetime m of such a tube that satisfies P(X > m) = 0.5.
Chapter 6 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.
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