Home
Class 12
MATHS
The random variable X has a probability ...

The random variable X has a probability distribution P(X) of the following form, where k is some number.
`P(X)={{:(k,",",if x=0),(2k,","," if x=1"),(3k,","," x=2 "),(0,",","otherwise"):}`
a. Determine the value of k
b. Find `P(X lt 2), IP(X le 2), P(X gt 2)`.

Text Solution

Verified by Experts

The correct Answer is:
(a) `k=(1)/(6)` (b)`P(X lt 2)=(1)/(2), P(X le 2)=1, P(X ge 2)=(1)/(2)`
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    NCERT TAMIL|Exercise EXERCISE 3.5|15 Videos

  • PROBABILITY

    NCERT TAMIL|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 13|19 Videos

  • PROBABILITY

    NCERT TAMIL|Exercise EXERCISE 3.3|14 Videos

  • ORDINARY DIFFERENTIAL EQUATIONS

    NCERT TAMIL|Exercise EXERCISE 10.9|25 Videos

  • PROBABILITY DISTRIBUTIONS

    NCERT TAMIL|Exercise EXERCISE 11.6 (Choose the Correct )|19 Videos

Similar Questions

Explore conceptually related problems

Let X denote the number of hours you study during a randomly selected school day. The probability that X can take the values x, has the following form, where k is some unknown constant. P(X=x)={{:(0.1,",",x=0),(kx,",","x=1 or 2"),(k(5-x),",","X=3 or 4 "),(0,",","otherwise"):} i. Find the value of k ii. What is the probability that you study atleast two hours? Exactly 2 hours? Atmost 2 hours?

A random variable X has the following probability mass function Find k

A random varibale x has the following probability mass function P(2 le X lt5)

A random variable X has the following probability distribution. i. k ii. P(X lt 3) iii. P (0 lt X lt 5)

A continuous random varibale X has probability density function f(x)=kx^(2) 0 le x lt 1 find k find P(X lt 5)

A random variable X has the following probability distribution. i. k, ii. P( X lt 3 ) iii. P( Xgt6 ) iv. (P( 0lt X lt 3 )

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

A continuous random varibale X has probability density function f(x)=kx^(2) 0 le x lt 1 find k P(1 lt x lt 5)

A random variable x has the following distribution . {:(x,1,2,3,4),(f(x),k,2k,4k,3k):} Then its mean is :

Determine the value of k for which x+2 is a factor of (x+1)^7+(2x+k)^3dot

NCERT TAMIL-PROBABILITY-EXERCISE 3.4
  1. State which of the following are not the probability distributions of ...

    Text Solution

    |

  2. An urn contains 5 red and 2 black balls. Two balls are randomly drawn....

    Text Solution

    |

  3. Let X represent the difference between the number of head and the numb...

    Text Solution

    |

  4. Find the probability distribution of i. number of head in two tosse...

    Text Solution

    |

  5. Find the probability distribution of the number of successes in two to...

    Text Solution

    |

  6. From a lot of 30 bulbs which include 6 defectives, a sample of 4 bulbs...

    Text Solution

    |

  7. A coin is biased so that the head is 3 times as likely to occur as tai...

    Text Solution

    |

  8. A random variable X has the following probability distribution. ...

    Text Solution

    |

  9. The random variable X has a probability distribution P(X) of the follo...

    Text Solution

    |

  10. Find the mean number of heads in three tosses of a fair coin.

    Text Solution

    |

  11. Two dice are thrown simultaneously. If X denotes the number of sixes, ...

    Text Solution

    |

  12. Two numbers are selected at random (without replacement) from the firs...

    Text Solution

    |

  13. Let X denote the sum of the numbers obtained when two fair dice are ro...

    Text Solution

    |

  14. A class has 15 students whose ages are 14, 17, 15, 14, 21, 17, 19, 20,...

    Text Solution

    |

  15. In a meeting, 70% of the members favour and 30% oppose a certain propo...

    Text Solution

    |

  16. The mean of the numbers obtained on throwing a die having written 1 on...

    Text Solution

    |

  17. Suppose that two cards are drawn at random from a deck of cards. Let X...

    Text Solution

    |