STA 119 Lecture Notes - Lecture 8: Random Variable

• School: University at Buffalo
• Department: Biostatistics
• Course: STA 119
• Professor: Kuhlmann Dietrich

Document Summary

We define the cumulative distribution function (cdf) of a random variable to the the function that tells us how much probability has accumulated up to and including that desired value of x. An uppercase letter (f) is used for the cdf. We get from the pdf to the cdf by accumulating (adding) probability. Example: determine the cdf of a random variable with the pmf given below x f(x) 1. 00 (cid:887)(cid:857)(cid:866)(cid:858) (cid:878) (cid:897)(cid:857)(cid:937) (cid:1540) (cid:866)(cid:858) (cid:878) . (cid:866)(cid:870) (cid:887)(cid:857)(cid:867)(cid:858) (cid:878) (cid:897)(cid:857)(cid:937) (cid:1540) (cid:867)(cid:858) (cid:878) . (cid:867)(cid:871) (cid:887)(cid:857)(cid:868)(cid:858) (cid:878) (cid:897)(cid:857)(cid:937) (cid:1540) (cid:868)(cid:858) (cid:878) . (cid:868)(cid:870) *** f(x) = all of the probability up to and including x has already been added. Example: use the cdf below to answer the probability questions x. [(---------5]------6)------7--------- (cid:887)(cid:857)(cid:871)(cid:858) (cid:887)(cid:857)(cid:870)(cid:858) (cid:878) . (cid:870)(cid:870) . (cid:870)(cid:865) (cid:878) . (cid:865)(cid:870) R(cid:886)(cid:894)(cid:886)(cid:894)b(cid:886)r(cid:875) (cid:887)(cid:857)(cid:871)(cid:858) (cid:878) (cid:897)(cid:857)(cid:905) (cid:1540) (cid:871)(cid:858) (cid:922)(cid:932) (cid:895)(cid:896)t (cid:897)(cid:857)(cid:905) (cid:878) (cid:871)(cid:858). I(cid:933) (cid:922)(cid:932) (cid:921)(cid:928)(cid:936) (cid:926)(cid:934)(cid:916)(cid:921) probability that has accumulated up to and including 6.