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# xid-7976602_1 - 1 Probability Density Functions from...

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Unformatted text preview: 1. Probability Density Functions from Chapter 4. In the Midterm exam, some density functions will be provided. You may be asked to fill in any of the additional information: the family names, the domain possible values, and the expected value and variance in terms of the parameters. Family Density function Domain E(X), V(X) Normal ¡¢£ ¤ ¥ ¦§¨¦©ª ¢ «¢¤ ¢ (- ¬­ ¬ª E(X) = μ V(X) = ®¯ ° Uniform ± ² ³ [A, B] E(X) = §´ µ ¶ª · ¸ ¹§ºª ® » ® §¶ ² ´ª ° «¼· Standard Beta §½ µ ¾ª §½ª ¿ §¾ª À ½¦ § ² Àª ¾¦ [0, 1] Á§ºª » ®Â §Â µ ®Ã ¸ ª Ä§Åª » ® ÂÃ §Â µ Ãª ° §Â µ Ã µ ¼ª Gamma ¾ ½ Æ§½ª ¨ ½¦ ¥ ¦ ¨ ¾ [0, ¬ª E(X) = α β V(X) = ®ÂÃ ° Exponential ®ÇÈ ¦É¨ [0, ¬ª E(X) = ¼ Ê ¸ V(X) = ¼ ¸ Ê ° Chi- squared ¢ Ë«¢ §Ì«¢ª À §Ë«¢ª¦ È ¦¨«¢ [0, ¬ª Gamma with α = ν/2, β=2 E(X) = ν , Var(X) = 2 ν Weibull ½ ¾ ½ ¨ ½¦ ¥ ¦§ ¨ ¾ ª ½ [0, ¬ª Not needed for exam Lognormal ¡¢£ ¤¨ ¥ ¦§ÍÎ§¨ª¦©ª...
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## This note was uploaded on 12/20/2011 for the course STAT 344 taught by Professor Staff during the Spring '08 term at George Mason.

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xid-7976602_1 - 1 Probability Density Functions from...

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