Results 1 to 3 of 3

Math Help - binomial

  1. #1
    Member
    Joined
    Aug 2007
    Posts
    239

    binomial

    50 (a)  b(3;8,0.6) = \binom{8}{3}(0.6)^{3}(0.4)^{5} - \binom{8}{2}(0.6)^{2}(0.4)^{6}

    (b)  b(5;8,0.6) = \binom{8}{5}(0.6)^{5}(0.4)^{3} - \binom{8}{4}(0.6)^{4}(0.4)^{4}

    (c)  P(3 \leq X \leq 5) = \binom{8}{5}(0.6)^{5}(0.4)^{3} - \binom{8}{2}(0.6)^{2}(0.4)^{6}

    (d)  P(1 \leq X) = \sum_{x=1}^{12} \binom{12}{x}(0.1)^{x}(0.9)^{12-x}

    59. (a)  B(4;10,0.3) = 0.850
    (b)  b(4;10,0.3) = B(4;10,0.3) - B(3;10,0.3) = 0.2
    (c)  b(6;10,0.7) = B(6;10,0.7) - B(5;10,0.7) = 0.2
    (d)  P(2 \leq X \leq 4) =  B(4;10,0.3) - B(1;10,0.3) = 0.701
    (e)  P(2 \leq X) = 1- P(X \leq 1) = 1 - B(1;10, 0.3) = 0.851
    (f)  P(X \leq 1) = B(1;10, 0.7) = 0

    (g)  P(2<X<6) = B(5;10,0.3) - B(2,10,0.3) = 0.570

    60. The long-run percentage of defectives is  5 \% . Also  X \sim \text{Bin}(25,.05) .
    (a)  P(X \leq 2) = B(2;25, .05) = 0.873
    (b)  P(X \geq 5) = 1-P(X \leq 4) = 1-B(4;25,.05)  = 1-0.993 = 0.007
    (c)  P(1 \leq X \leq 4) = B(4;25,.05) - B(0;25,.05)

    these look right?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by shilz222 View Post
    50 (a)  b(3;8,0.6) = \binom{8}{3}(0.6)^{3}(0.4)^{5} - \binom{8}{2}(0.6)^{2}(0.4)^{6}
    By definition:

    (a)  b(3;8,0.6) = \binom{8}{3}(0.6)^{3}(0.4)^{5}

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by shilz222;106361 (c) [tex
    P(3 \leq X \leq 5) = \binom{8}{5}(0.6)^{5}(0.4)^{3} - \binom{8}{2}(0.6)^{2}(0.4)^{6} [/tex]
    If X\sim B(8,0.6):

     P(3 \leq X \leq 5) = \binom{8}{5}(0.6)^{5}(0.4)^{3} +\binom{8}{4}(0.6)^{4}(0.4)^{4}+\binom{8}{3}(0.6)^  {3}(0.4)^{5}

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: July 15th 2010, 05:33 AM
  2. Replies: 1
    Last Post: November 12th 2009, 12:38 AM
  3. Binomial Theorem or Binomial Coefficient
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: October 2nd 2009, 01:06 PM
  4. Replies: 1
    Last Post: March 11th 2009, 11:09 PM
  5. Relation between Negative Binomial and Binomial Distros
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: November 5th 2007, 06:59 AM

Search Tags


/mathhelpforum @mathhelpforum