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zhYv~*gdqyjz;6CE+W&Y$u<8d&>6r?>_y4a9vMqLb{ocJt7ZSp6l>Rk@|4#-i8fH{X zRY`z@5d`-LiQ^B6>EGFkCHsEmK&m7g_Om}tUG)RD1cpRPQB_zsCJx#ElR4f#En6$k8&hM!E&IS`P z?#3a@jZO5Yao~Y*$c7q_etYl-d%br*3r=mWeL>|=uhS&2FxeE z;vMN9%?AO ((648d1aea-71f3-473b-8e72-d1ee4e629a91)) + id:: 648d1aec-b256-4d1b-91d7-9a22cc30657e - ((648d1b0d-fdbf-4373-84a8-a072590881a1)) - Standard distribution ((648d1f39-bc89-4efe-98b3-1c654716cf65)) - Properties collapsed:: true - mean and variance :-> ((648d1bfd-fcfb-43ed-801e-0de972c24cb1)) + id:: 648d1c05-1299-42a9-80e0-d877610aa19d - Exponential Distribution similar to -> ((648c650a-e188-49a6-9f89-9a3407057ddf)) collapsed:: true - Definition: #flashcard + id:: 648d2593-394c-4b31-a1a4-4eef625eacac collapsed:: true - ((648d25a0-12d9-47c5-b9ca-f7cafdf15d89)) - Properties collapsed:: true - Mean, variance :-> ((648d25a0-12d9-47c5-b9ca-f7cafdf15d89)) + id:: 648d25a3-9cae-4c50-a073-749b5e364bcb - Memory-less #flashcard + id:: 648d26a1-d047-40e6-bcc5-9fab241c9a37 collapsed:: true - ((648d26c8-0292-4c02-8d6e-2b4f5cb10385)) - LATER Example: connection between Poisson and Exponential distribution @@ -2841,6 +2846,7 @@ - Normal Distribution collapsed:: true - Definition #flashcard + id:: 648d288a-4a44-443d-8490-500ddd24bed4 collapsed:: true - ((648d2884-c239-4d00-9b6f-291bf4280dab)) - Properties: @@ -2848,18 +2854,23 @@ - ((648d2931-ae90-414a-b12c-e19aa1c534fc)) - ((648d294d-7bb2-4b6e-8aca-70dc4af6005c)) - Standard normal distribution :-> ((648d2960-d588-4610-a643-e292ef5b793f)) + id:: 648d2951-61a2-4545-b1ee-d159f9ba1037 - Calculating distribution between certain intervals :-> ((648d29b2-c64e-4480-b633-169fe5f0b6cd)) id:: 648d29b8-bd11-4eb6-9240-941c2ff636f1 - Calculating negative ones :-> ((648d29da-0535-4dd3-ae79-48b34e047339)) + id:: 648d29dc-8de6-44f5-b969-b341fc06a966 - (Some sort of ) linearity :-> ((648d2d62-f5e5-491f-ae12-e9638ee75f7c)) + id:: 648d2d49-79da-40fc-a205-3aa0f52eb770 - Example collapsed:: true - in specified interval ((648d2c35-041a-4575-b39d-c42c1a6f532f)) - without knowing $$\mu$$ and $$\sigma$$: ((648d2cfd-2cef-48d2-b791-e5ac01e43fd8)) #flashcard + id:: 648d2c39-55dd-4cfd-9a39-1c17d90ff3e3 collapsed:: true - ((648d2cfd-2cef-48d2-b791-e5ac01e43fd8)) - - ==Summary== #flashcard Bernoulli, Binomial, Geometric, Poisson, Uniform, Exponential, Normal + id:: 648d2da0-7c8a-4635-b8b7-9ec0d72efc21 - ((648d2dcb-a1da-4b22-99c8-ddcc0f059cff)) - LATER Ch3 Random Vectors collapsed:: true @@ -2880,6 +2891,7 @@ - ((648d4b7a-64fa-4e2a-a5db-4970c647527c)) - LATER Examples ((648d4dce-72e2-4d0b-a70e-fefaa2b1ee4c)) #flashcard extra:: f(-inf , y ) = 0 + id:: 648d4d7d-88ed-4993-b4ea-95172bd9315d collapsed:: true - ((648d4dd7-6ecc-479d-bd1e-0280c9bb7155)) - Discrete random vectors @@ -2920,6 +2932,7 @@ - Discrete case collapsed:: true - Definition: #flashcard, similar to ((648c1481-86ac-4efa-a60a-f4787d942d76)) + id:: 648d5f70-6c2a-4cb7-b6f8-139acccd9c9c collapsed:: true - ((648d6291-12ed-4dfb-8ade-42556f17d91a)) - Example: ((648d668a-02de-4e33-b5fe-b78b25a57b78)) @@ -2950,15 +2963,18 @@ - $X + Y$ - ((648d718a-6ea6-45b9-96f7-2f89ecbf54f3)) - Can be written as: #flashcard + id:: 648d71a6-3a5b-4ef8-b461-ab67f9b65332 - ((648d71bc-ca55-46f9-a7d4-22a339a7f9c0)) - Also: ((648d71dd-ce78-49c5-a12c-58dea53bd4cc)) - Examples - Uniform distribution: - ((648d767e-8555-4232-8be8-ff27073ed790)) - Exponential distribution : 知道过程结果 #flashcard + id:: 648d7634-ca1e-4b05-ae6d-dadaab66fb07 - ((648d7691-7c7f-435a-a441-0a4314fd9e60)) - - Normal distribution: 记结论 - - + - Normal distribution: 记结论 #flashcard + id:: 648d763a-2c89-4ec8-b09c-f034965f56c8 + - ((648d769d-a3ea-4e6c-bc93-564d88d6ed38)) - $min(X,Y)$ - - $max(X, Y)$