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Clash Royale CLAN TAG #URR8PPP up vote 0 down vote favorite I need help in finding the variance of a joint probability function. The probability density function in this case is $f(x)$ which is created by $$frac125x^218,; 0le xle 0.6,;frac910x^2,; (0.6le xle 0.9), text and 0 text elsewhere.$$ I know how to find the variance for a single probability function, however not when they consist of two functions. Help will be appreciated. Thanks. variance share | cite | improve this question edited Aug 29 at 11:23 amWhy 190k 26 221 433 asked Aug 29 at 10:45 Deep Patel 6 3 Use $Var[X] = E[X^2] - (E[X])^2$ – the man Aug 29 at 11:06 That is not a joint probability function. It is a piecewise function. – Graham Kemp Aug 29 at 11:34 add a comment  |  up vote 0 down vote favorite I need help in finding the variance of a joint...

Clash Royale CLAN TAG #URR8PPP up vote 0 down vote favorite Consider the following autonomous vector field: $$dot x = −x$$ $$dot y = sin y$$ where $x in mathbbR^2, -pi ≤ y ≤ pi$ $bullet$ Find all fixed points. $bullet$ Determine the linearized stability properties of each fixed point. $bullet$ Determine the global stable and unstable manifolds of the origin. $bullet$ Determine whether any nonhyperbolic fixed points are stable or unstable? (You must justify your answer.) ATTEMPT : $bullet$ Fixed points: $(0, -pi), (0,0), (0,pi)$ $bullet$ Linearisation by the Jacobian: $J = beginpmatrix-1 & 0 \ 0 & cos y endpmatrix$ So we have: $J(0,-pi) = beginpmatrix-1 & 0 \ 0 & -1endpmatrix$, $J(0,0) = beginpmatrix-1 & 0 \ 0 & 1 endpmatrix$, $J(0,pi) = beginpmatrix-1 & 0 \ 0 & -1endpmatrix$ Which represent a sink (stable), a saddle (unstable), and a sink...