The document discusses discrete and continuous random variables. It defines discrete and continuous random variables and their probability distributions. Specifically, it discusses probability mass functions for discrete random variables and probability density functions for continuous random variables. It also discusses how to compute the expected value and variance of discrete and continuous random variables.

1. Pertemuan 10 VARIAB E L ACAK DISKRIT DAN KONTINU Hdi Nasbey, M.Si Jurusan Fisika Fakultas Matematika dan Ilmu Pemgetahuan Alam

10. Computing the Mean for Investment Returns Return per $1,000 for two types of investments P( X i ) P( Y i ) Economic Condition Dow Jones Fund X Growth Stock Y .2 .2 Recession -$100 -$200 .5 .5 Stable Economy + 100 + 50 .3 .3 Expanding Economy + 250 + 350 Investment 01/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

11. Computing the Variance for Investment Returns P( X i ) P(Y i ) Economic Condition Dow Jones Fund X Growth Stock Y .2 .2 Recession -$100 -$200 .5 .5 Stable Economy + 100 + 50 .3 .3 Expanding Economy + 250 + 350 Investment 01/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

12. Continuous Random Variables A random variable X is continuous if its set of possible values is an entire interval of numbers (If A < B , then any number x between A and B is possible). 01/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

14. Probability Distribution Let X be a continuous rv. Then a probability distribution or probability density function (pdf) of X is a function f ( x ) such that for any two numbers a and b , The graph of f is the density curve . 01/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

15. Probability Density Function is given by the area of the shaded region. b a 01/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

17. Ex 1 . (4.1) X = amount of time for which a book on 2-hour reserve at a college library is checked out by a randomly selected student and suppose that X has density function. 01/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

18. Probability for a Continuous rv If X is a continuous rv, then for any number c , P ( x = c ) = 0. For any two numbers a and b with a < b, 01/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

20. Variance and Standard Deviation The variance of continuous rv X with pdf f ( x ) and mean is The standard deviation is 01/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

21. Short-cut Formula for Variance 01/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |