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 June 5th, 2018, 12:00 AM #1 Newbie   Joined: Jun 2018 From: seoul Posts: 1 Thanks: 1 How can I calculate the joint probability for three variable? I am a student studying the joint probability density function with multi variables. I understand how to obtain a joint probability density function when two uniform distributions have the following joint distribution like below. The distribution $f_V$(v) can be determined based on the distribution of $t$, denoted as $f_T$(t),and that of $c_i$, denoted by $f_C$(c). The distributions $f_T$(t) and $f_C$(c) are available, e.g., based on the previous observations. Assume that variables $t$ and $c$ are independent from each other and follow uniform distributions, i.e., $t$~ $U[t_{min}; t_{max}]$ and $c$~ $U[c_{min}; c_{max}]$, $c_{min}$ > 0. Then, $f_V$ (v) is determined as follows. Let, z = c, v = $\frac{t}{c}$ and we have t = vz and c = z. Jacobian determinant $J_D$ among t, c, v and z is given by $J_D$ = z. So, the PDF for joint distribution $(v,z)$ is given by $f_{V,Z}$(v,z) = $f_T$(v,z)$f_C$(z)$|J_D|$ = $\frac{1}{(t_{max} - t_{min})(c_{max}-c_{min})}|z|$. So, the distribution of $v$, $f_V$(v) is determined by $f_V$(v) = $\int_{-\infty}^\infty$ $f_{V,Z}$(v,z) $dz$ = $\int_{c_{min}}^{c_{max}}$ $f_{V,Z}$(v,z)$dz$ = $\frac{c_{min}+c_{max}}{2(t_{max}-t_{min})}$ The question is based on above understanding, I try to do calculations when there are 3 variables. The distribution $f_V$(v) can be determined based on the distribution of $t$, denoted as $f_T$(t), that of $c$, denoted by $f_C$(c) and that of $L$, denoted by $f_L$(l). The distributions $f_T$(t), $f_C$(c), and $f_L$(l) are available. Assume that variables $t$,$c$ and $l$ are independent from each other and follow uniform distributions, i.e., $t$~ $U[t_{min}; t_{max}]$ and $c$~ $U[c_{min}; c_{max}]$, $c_{min}$ > 0, $l$~ $U[l_{min}; l_{max}]$. Then, how can i determined $f_V$ (v)? Can I get a guide for determining this joint probability function or some materials i can follow the step for this? Let z = c, v = $\frac{t}{c*l}$ and we have t = $vzl$ and c = z. Thanks from Shanonhaliwell Tags calculate, joint, probability, variable Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post fun Probability and Statistics 6 January 25th, 2018 04:54 PM Runner8806 Probability and Statistics 1 April 9th, 2017 12:32 PM sau Probability and Statistics 1 May 23rd, 2014 04:56 PM token22 Advanced Statistics 2 April 26th, 2012 03:28 PM Dontlookback Probability and Statistics 5 December 7th, 2010 01:00 PM

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