Home
Class 12
MATHS
A rod of length 2l is broken into two pi...

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 lt x ge l), (0, l le x lt 2l):}`
The mean and variance of the shorter of the two pieces are respectively

A

`(l)/(2),(l^(2))/(3)`

B

`(l)/(2),(l^(2))/(6)`

C

`l,(l^(2))/(12)`

D

`(l)/(2),(l^(2))/(12)`

Text Solution

Verified by Experts

The correct Answer is:
d
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY DISTRIBUTIONS

    PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE|40 Videos

  • PROBABILITY DISTRIBUTIONS

    PREMIERS PUBLISHERS|Exercise EXERCISE 11.5|18 Videos

  • ORDINARY DIFFERENTIAL EQUATIONS

    PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE (ANSWER THE FOLLOWING QUESTIONS )|22 Videos

  • THEORY OF EQUATIONS

    PREMIERS PUBLISHERS|Exercise Problems for practice (Answer the following)|21 Videos

Similar Questions

Explore conceptually related problems

The probability density function of the random variable X is given by f(x)={{:(16xe^(-4x), "for " x gt 0), (0, "for " x le 0):} find the mean and variance of X

The probability density function of X is given by f(x)={{:(ke^(-x/3), "for " x gt 0), (0, "for " x le 0):} Find P(X lt 3)

The probability density function of X is f(x)={{:(x, 0 lt x lt 1), (2-x, 1 le x lt 2), (0, "otherwise"):} Find P(0.2 le X lt 0.6)

The probability density function of X is f(x)={{:(x, 0 lt x lt 1), (2-x, 1 le x lt 2), (0, "otherwise"):} Find P(0.5 le X lt 1.5)

The probability density function of X is f(x)={{:(x, 0 lt x lt 1), (2-x, 1 le x lt 2), (0, "otherwise"):} Find P(1.2 le X lt 1.8)

Draw the graph of the function f(x ) = {{:(1+x , -1 le x le 0),( 1-x, 0 lt x le 1):}

If f(x)=ae^(-2x)0ltxltinfty is a probability density function of a random variable x then its variance is

A continuous random varibale X has probability density function f(x)=kx^(2) 0 le x lt 1 find k (X gt6)

PREMIERS PUBLISHERS-PROBABILITY DISTRIBUTIONS-EXERCISE 11.6
  1. Let X be random variable with probability density function f(x)={{:(...

    Text Solution

    |

  2. A rod of length 2l is broken into two pieces at random. The probabilit...

    Text Solution

    |

  3. Consider a game where the player tosses a six sided fair die. If the f...

    Text Solution

    |

  4. A pair of dice numbered 1, 2, 3, 4, 5, 6 of a six-sided die and 1, 2, ...

    Text Solution

    |

  5. A random variable X has binominal distribution with n = 25 and p = 0.8...

    Text Solution

    |

  6. Let X represent the difference between the number of heads and the nu...

    Text Solution

    |

  7. If the function f(x)=1/12 " for " a lt x lt b, represents a probabilit...

    Text Solution

    |

  8. Four buses carrying 160 students from the same school arrive at a foot...

    Text Solution

    |

  9. Two coins are to be flipped. The first coin will land on heads with pr...

    Text Solution

    |

  10. On a multiple-choice exam with 3 possible destructive for each of the ...

    Text Solution

    |

  11. If P{X=0}=1-P{X=1}. If E{X}=3Var(X), then P{X=0} is

    Text Solution

    |

  12. If X is a binomial random variable with expected value 6 and variance ...

    Text Solution

    |

  13. The random variable X has the probability density function f(x)={{:(ax...

    Text Solution

    |

  14. Suppose that X takes on one of the values 0, 1, and 2. If for some con...

    Text Solution

    |

  15. Which of the following is a discrete random variable? I. The number ...

    Text Solution

    |

  16. If f(x)={{:(2x, 0 le x le a), (0, "otherwise"):} is a probability dens...

    Text Solution

    |

  17. The probability function of a random variable is defined as The...

    Text Solution

    |

  18. Let X have a Bernoulli distribution with mean 0.4, then the variance ...

    Text Solution

    |

  19. If in 6 trials, X is a binomial variate which follows the relation 9P(...

    Text Solution

    |

  20. A computer salesperson knows from his past experience that he sells co...

    Text Solution

    |