Advertisements
Advertisements
प्रश्न
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
Advertisements
उत्तर
Let X be the random variable
`"E"(x) = int_(oo)^oo x"f"(x) "d"x`
`"E"(x) = int_0^oo x[2"e"^(2x) "d"]x`
= `2int_0^x x"e"^(-2x) "d"x` ......`{int_0^oo x^"n""e"^(-oox) "d"x = ("n"!)/(oo^("n" + 1))}`
= `2[(1!)/(2)]`
= `2[1/4]`
= `1/2`
∴ `"E"(x) = 1/2`
Here n = 1, `oo` = 2
APPEARS IN
संबंधित प्रश्न
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
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
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
Find the expected value for the random variable of an unbiased die
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
In investment, a man can make a profit of ₹ 5,000 with a probability of 0.62 or a loss of ₹ 8,000 with a probability of 0.38. Find the expected gain
How do you defi ne variance in terms of Mathematical expectation?
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:
Probability which explains x is equal to or less than a particular value is classified as
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
