Problem 4. Let X have density f(x) = cx²(1-x)² for 0≤ x ≤ 1, and f(x) = 0 elsewhere. (1) Find c. (2) Calculate E(X). (3) Calculate V(X).
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- YOUR TURN Suppose x are y are both functions of t and x3+2xy+y2=1. If x=1, y=2, and dxdt=6, then find dydt.Plant Growth Researchers have found that the probability P that a plant will grow to radius R can be described by the differential equation dPdR=4DRP2 where D is the density of the plants in an area. Source: Ecology. Given the initial condition P(0)=1, find a formula for P in term of R.