In Problem 22, find d so that the probability of a randomly selected laser pointer battery lasting d years or less is .5. 22. 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).
In Problem 22, find d so that the probability of a randomly selected laser pointer battery lasting d years or less is .5. 22. 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 calculates that the probability of randomly selected laser pointer battery lasting d years or less is 0.5.
4. The lifetime in hours of an electronic gadget is a random variable having a
probability density function of
x2 0.
Compute the expected lifetime of such a gadget.
f(x) = xe-2x
Suppose that the random variable X has the probability density function
f(x) = {"
c(1- x2)
for - 1s x s1
elsewhere
What is the variance of X
A
1/2
B
1/3
1/5
D
1/4
2. If the random variable X has the
probability density function
f(x) = (1-x²), -1 < x < 1,
3
4
what is the variance of 15X + 2?
Chapter 6 Solutions
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