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Let X be random variable with probabilit...

Let X be random variable with probability density function
`f(x)={{:(2/x^(3), x ge 1), (0, x lt 1):}`
Which of the following statement is correct

A

both mean and variance exist

B

mean exists but variance does not exist

C

both mean and variance do not exist

D

variance exists but mean does not exist

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Knowledge Check

  • Let X be random variable with probability density function f(x)={{:((2)/(x^(3)),xge1),(0,xlt1):} Which of the following statement is correct

    A
    both mean and variance exist
    B
    mean exists but variance does not exist
    C
    both mean and variance do not exist
    D
    variance exists but Mean does not exist.

  • A discrete random variable X has probability mass function P(x) then

    A
    `0lep(x)le1`
    B
    `p(x)ge1`
    C
    `p(x)le0`
    D
    `(pi)/(2)`

  • The random variable X has the probability density function f(x)={{:(ax+b, 0 lt x lt 1), (0, "otherwise"):} and E(X)=7/12 , then a and b are respectively

    A
    `1 " and " 1/2`
    B
    `1/2 " and " 1`
    C
    2 and 1
    D
    1 and 2

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    If X is the random variable with probability density function f(x) is given by f(x)={{:(x+1, -1 le x lt 0), (-x+1, 0 le x lt 1), (0,"otherwise"):} then find (i) the distribution function F(x) (ii) P(-0.5 le X le 0.5)

    Find the mean of a random variable X, whose probability density function is f(x)={{:(lambdae^(-lambdax), "for " x ge 0), (0, "otherwise"):} .

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