Advertisements
Advertisements
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"):}`
Advertisements
उत्तर
Mean: `mu = "E"("X")`
= `int_(1/2)^2 x f(x) "d"x`
= `int_1^(1/2) x xx 2(x - 1) "d"x`
= `2 int_1^2 (x^2 - x) "d"x`
= `2[x^3/3 - x^2/2]_1^2`
= `2[8/3 - 4/2 - 1/3 + 1/2]`
= `2(7/3 - 3/2)`
= `2 xx 5/6`
= `5/3`
Variance: `"E"("X"^2)`
= `int_1^2 x^2 f(x) "d"x`
= `2int_1^2 (x^3 - x^2) "d"x`
= `2[x^4/4 - x^3/3]_1^2`
= `2[16/4 - 8/3 - 1/4 + 1/3]`
= `2[15/4 - 7/3]`
= `2 xx 17/12`
= `17/6`
Var(X) = `"E"("X"^2) - ["E"("X")]^2`
= `17/6 - (5/3)^2`
= `17/6 - 25/9`
= `(51 - 50)/18`
= `1/18`
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):}`
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) = {{:(1/2 "e"^(x/2), "for" x > 0),(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
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
Find the expected value for the random variable of an unbiased die
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 |
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
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
What are the properties of Mathematical expectation?
State the definition of Mathematical expectation using continuous random variable
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:
If X is a discrete random variable and p(x) is the probability of X, then the expected value of this random variable is equal to
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 listing of all the outcomes of an experiment and the probability associated with each outcome is called
Choose the correct alternative:
If p(x) = `1/10`, x = 10, then E(X) 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)
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
