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) = {{:((4 - x)/6, x = 1"," 2"," 3),(0, "otherwise"):}`
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"):}`
Four fair coins are tossed once. Find the probability mass function, mean and variance for a number of heads that occurred
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:
Consider a game where the player tosses a six-sided fair die. If the face that comes up is 6, the player wins ₹ 36, otherwise he loses ₹ k2, where k is the face that comes up k = {1, 2, 3, 4, 5}. The expected amount to win at this game in ₹ is
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
Find the expected value for the random variable of an unbiased die
What do you understand by Mathematical expectation?
In a business venture a man can make a profit of ₹ 2,000 with a probability of 0.4 or have a loss of ₹ 1,000 with a probability of 0.6. What is his expected, variance and standard deviation of profit?
The number of miles an automobile tire lasts before it reaches a critical point in tread wear can be represented by a p.d.f.
f(x) = `{{:(1/30 "e"^(- x/30)",", "for" x > 0),(0",", "for" x ≤ 0):}`
Find the expected number of miles (in thousands) a tire would last until it reaches the critical tread wear point
Let X be a random variable and Y = 2X + 1. What is the variance of Y if variance of X is 5?
Choose the correct alternative:
E[X – E(X)] is equal to
Choose the correct alternative:
A discrete probability function p(x) is always non-negative and always lies between
Prove that if E(X) = 0, then V(X) = E(X2)
What is the expected value of a game that works as follows: I flip a coin and if tails pay you ₹ 2; if heads pay you ₹ 1. In either case, I also pay you ₹ 0.50
Prove that V(X + b) = V(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
