Results 1 to 2 of 2

Math Help - Help random variable

  1. #1
    Newbie
    Joined
    Oct 2007
    Posts
    9
    Thanks
    1

    Help random variable

    The probability that a patient recovers from a stomach disease is .8. Suppose 20 people are known to have contracted this disease.

    Let X = # of people who recover out of 20 contracted the disease
    while PMF for X and solve problems. Assume that sample of size 20 is independently selected.

    A. What is the probability that exactly 14 recover?
    B. What is the probability that at least 10 recover?
    C. What is the probability that at least 14 but not more than 18 recover?
    D. What is the probability that at most 16 recover?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by ballinisahobby View Post
    The probability that a patient recovers from a stomach disease is .8. Suppose 20 people are known to have contracted this disease.

    Let X = # of people who recover out of 20 contracted the disease
    while PMF for X and solve problems. Assume that sample of size 20 is independently selected.
    we can use Bernoulli trials here.

    recall that by the method of Bernoulli Trials we have that, the probability of k successes in n trials is given by:

    P(k) = {n \choose k}p^kq^{n-k}

    where p is the probability of success, and q = 1 - p is the probability of failure.

    Let recovery be a success here. thus p = 0.8, and q = 0.2 and n = 20

    A. What is the probability that exactly 14 recover?
    this is P(X = 14)

    B. What is the probability that at least 10 recover?
    this is P(X \ge 10) = P(10) + P(11) + P(12) + ... + P(20)

    C. What is the probability that at least 14 but not more than 18 recover?
    this is P(14 \le X \le 18) = P(14) + P(15) + ... + P(18)

    D. What is the probability that at most 16 recover?
    this is P(X \le 16) = 1 - P(X > 16) = P(17) + P(18) + P(19) + P(20)


    this is a lot of computation, but you can reuse values, so it's not that bad
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: October 15th 2012, 11:37 PM
  2. exponential random variable with a random mean?
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: March 21st 2010, 03:05 PM
  3. Replies: 9
    Last Post: January 28th 2010, 08:26 AM
  4. Replies: 3
    Last Post: January 13th 2010, 11:44 AM
  5. Mean of random variable
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: March 31st 2008, 09:42 PM

Search Tags


/mathhelpforum @mathhelpforum