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
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
Four fair coins are tossed once. Find the probability mass function, mean and variance for a number of heads that occurred
The following table is describing about the probability mass function of the random variable X
| x | 3 | 4 | 5 |
| P(x) | 0.2 | 0.3 | 0.5 |
Find the standard deviation of x.
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 do you understand by Mathematical expectation?
Define Mathematical expectation in terms of discrete random variable
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:
Which of the following is not possible in probability distribution?
Choose the correct alternative:
The distribution function F(x) is equal to
