Advertisements
Advertisements
Question
Let X be a continuous random variable with probability density function
`"f"_x(x) = {{:(2x",", 0 ≤ x ≤ 1),(0",", "otherwise"):}`
Find the expected value of X
Solution
Let x be a continuous random variable.
In the probability density function,
Expected Value E(x) = `int_(-oo)^oo x"f"(x) "d"x`
Here E(x) = `int_0^1 x(2x) "d"x = int_0^1 2x^2 "d"x`
= `2[x^3/3]_0^1`
= `2/3[x^3]_0^1`
= `2/3 [1 - 0]`
= `2/3`
∴ E(x) = `2/3`
APPEARS IN
RELATED QUESTIONS
For the random variable X with the given probability mass function as below, find the mean and variance.
`f(x) = {{:(1/2 "e"^(x/2), "for" x > 0),(0, "otherwise"):}`
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
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
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 |
What do you understand by Mathematical expectation?
How do you defi ne variance in terms of Mathematical expectation?
Choose the correct alternative:
Given E(X) = 5 and E(Y) = – 2, then E(X – Y) is
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
