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) = {{:(1/10, x = 2"," 5),(1/5, x = 0"," 1"," 3"," 4):}`
Four fair coins are tossed once. Find the probability mass function, mean and variance for a number of heads that occurred
A commuter train arrives punctually at a station every half hour. Each morning, a student leaves his house to the train station. Let X denote the amount of time, in minutes, that the student waits for the train from the time he reaches the train station. It is known that the pdf of X is
`f(x) = {{:(1/30, 0 < x < 30),(0, "elsewhere"):}`
Obtain and interpret the expected value of the random variable X
The probability density function of the random variable X is given by
`f(x) = {{:(16x"e"^(-4x), x > 0),(0, x ≤ 0):}`
find the mean and variance of 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:
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
Choose the correct alternative:
If X is a binomial random variable with I expected value 6 and variance 2.4, Then P(X = 5) is
How do you defi ne variance in terms of Mathematical expectation?
Define Mathematical expectation in terms of discrete random variable
Choose the correct alternative:
Given E(X) = 5 and E(Y) = – 2, then E(X – Y) is
Choose the correct alternative:
If X is a discrete random variable and p(x) is the probability of X, then the expected value of this random variable is equal to
Choose the correct alternative:
Which of the following is not possible in probability distribution?
Choose the correct alternative:
E[X – E(X)] is equal to
Choose the correct alternative:
A listing of all the outcomes of an experiment and the probability associated with each outcome is called
Choose the correct alternative:
If p(x) = `1/10`, x = 10, then E(X) is
Choose the correct alternative:
An expected value of a random variable is equal to it’s
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
