Advertisements
Advertisements
Question
Choose the correct alternative:
Let X be random variable with probability density function
`f(x) = {(2/x^3, x ≥ 1),(0, x < 1):}`
Which of the following statement is correct?
Options
Both mean and variance exist
Mean exists but variance does not exist
Both mean and variance do not exist
Variance exists but mean does not exist.
Solution
Mean exists but variance does not exist
APPEARS IN
RELATED QUESTIONS
The probability density function of X is given by
`f(x) = {{:(kx"e"^(-2x), "for" x > 0),(0, "for" x ≤ 0):}`
Find the value of k
The probability density function of X is `f(x) = {(x, 0 < x < 1),(2 - x, 1 ≤ x ≤ 2),(0, "otherwise"):}`
Find P(0.2 ≤ X < 0.6)
The probability density function of X is `f(x) = {(x, 0 < x < 1),(2 - x, 1 ≤ x ≤ 2),(0, "otherwise"):}`
Find P(1.2 ≤ X < 1.8)
The probability density function of X is `f(x) = {(x, 0 < x < 1),(2 - x, 1 ≤ x ≤ 2),(0, "otherwise"):}`
Find P(0.5 ≤ X < 1.5)
Suppose the amount of milk sold daily at a milk booth is distributed with a minimum of 200 litres and a maximum of 600 litres with probability density function
`f(x) = {{:(k, 200 ≤ x ≤ 600),(0, "otherwise"):}`
Find the value of k
The probability density function of X is given by
`f(x) = {(k"e"^(- x/3), "for" x > 0),(0,"for" x ≤ 0):}`
Find the value of k
The probability density function of X is given by
`f(x) = {(k"e"^(- x/3), "for" x > 0),(0,"for" x ≤ 0):}`
Find P(5 ≤ X)
The probability density function of X is given by
`f(x) = {(k"e"^(- x/3), "for" x > 0),(0,"for" x ≤ 0):}`
Find P(X ≤ 4)
If X is the random variable with probability density function f(x) given by,
`f(x) = {{:(x + 1",", -1 ≤ x < 0),(-x +1",", 0 ≤ x < 1),(0, "otherwise"):}`
then find the distribution function F(x)
If X is the random variable with probability density function f(x) given by,
`f(x) = {{:(x + 1",", -1 ≤ x < 0),(-x +1",", 0 ≤ x < 1),(0, "otherwise"):}`
then find P(– 0.5 ≤ x ≤ 0.5)
If X is the random variable with distribution function F(x) given by,
F(x) = `{{:(0",", - oo < x < 0),(1/2(x^2 + x)",", 0 ≤ x ≤ 1),(1",", 1 ≤ x < oo):}`
then find P(0.3 ≤ X ≤ 0.6)
Choose the correct alternative:
A rod of length 2l is broken into two pieces at random. The probability density function of the shorter of the two pieces is
`f(x) = {{:(1/l, 0 < x < l),(0, l ≤ x < 2l):}`
The mean and variance of the shorter of the two pieces are respectively
Choose the correct alternative:
If `f(x) = {{:(2x, 0 ≤ x ≤ "a"),(0, "otherwise"):}` is a probability density function of a random variable, then the value of a is
Choose the correct alternative:
A computer salesperson knows from his past experience that he sells computers to one in every twenty customers who enter the showroom. What is the probability that he will sell a computer to exactly two of the next three customers?
