Advertisements
Advertisements
Question
The time to failure in thousands of hours of an electronic equipment used in a manufactured computer has the density function
`f(x) = {{:(3"e"^(-3x), x > 0),(0, "eleswhere"):}`
Find the expected life of this electronic equipment
Advertisements
Solution
`mu = "E"("X")`
= `int_0^oo x f(x) "d"x`
= `3 int_0^oo x"e"^(-3x) "d"x`
u = x, `int"dv" = int"e"^(-3x)"d"x`
du = dx, v = `"e"^(-3x)/(-3)`
`int"udv" = "uv" - int"vdu"`
= `3[(x"e"^(-3x))/(-3) + int"e"^(-3x)/3 "d"x]_0^oo`
= `3[- (x"e"^(-3x))/3 - "e"^(-3x)/9]_0^oo`
= `3[0 - (0 - 1/9)]`
= `1/3`
Expected life of the electronic equipment = `1/3`
APPEARS IN
RELATED QUESTIONS
For the random variable X with the given probability mass function as below, find the mean and variance.
`f(x) = {{:(2(x - 1), 1 < x ≤ 2),(0, "otherwise"):}`
Two balls are drawn in succession without replacement from an urn containing four red balls and three black balls. Let X be the possible outcomes drawing red balls. Find the probability mass function and mean for X
A lottery with 600 tickets gives one prize of ₹ 200, four prizes of ₹ 100, and six prizes of ₹ 50. If the ticket costs is ₹ 2, find the expected winning amount of a ticket
Choose the correct alternative:
Four buses carrying 160 students from the same school arrive at a football stadium. The buses carry, respectively, 42, 36, 34, and 48 students. One of the students is randomly selected. Let X denote the number of students that were on the bus carrying the randomly selected student. One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on that bus. Then E(X) and E(Y) respectively are
Choose the correct alternative:
On a multiple-choice exam with 3 possible destructive for each of the 5 questions, the probability that a student will get 4 or more correct answers just by guessing is
Let X be a continuous random variable with probability density function
f(x) = `{{:(3/x^4",", x ≥ 1),(0",", "otherwise"):}`
Find the mean and variance of X
What are the properties of Mathematical expectation?
How do you defi ne variance in terms of Mathematical expectation?
A person tosses a coin and is to receive ₹ 4 for a head and is to pay ₹ 2 for a tail. Find the expectation and variance of his gains
Choose the correct alternative:
Value which is obtained by multiplying possible values of a random variable with a probability of occurrence and is equal to the weighted average is called
Choose the correct alternative:
Given E(X) = 5 and E(Y) = – 2, then E(X – Y) is
Choose the correct alternative:
A discrete probability distribution may be represented by
Choose the correct alternative:
E[X – E(X)] is equal to
Choose the correct alternative:
An expected value of a random variable is equal to it’s
Choose the correct alternative:
A discrete probability function p(x) is always non-negative and always lies between
Prove that V(aX) = a2V(X)
The time to failure in thousands of hours of an important piece of electronic equipment used in a manufactured DVD player has the density function
f(x) = `{{:(2"e"^(-2x)",", x > 0),(0",", "otherwise"):}`
Find the expected life of this piece of equipment
