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) = {{:(1/10, x = 2"," 5),(1/5, x = 0"," 1"," 3"," 4):}`
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
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
Let X be a random variable defining number of students getting A grade. Find the expected value of X from the given table:
| X = x | 0 | 1 | 2 | 3 |
| P(X = x) | 0.2 | 0.1 | 0.4 | 0.3 |
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?
Choose the correct alternative:
E[X – E(X)] is equal to
Choose the correct alternative:
E[X – E(X)]2 is
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)
Prove that V(X + b) = V(X)
