3. A individual visits a large mango orchard with very large number of very large trees, where the probability of picking a ripe mango is p and is independent of other picked mangoes. The individual decides to pick ripe mangoes ...
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2. Consider the following joint distribution of random variables X and Y. Y a. Find Px(x). b. Calculate E[X]. c. Let Z = max(X,Y). Find Pz(z). d. What is E[Z]? e. Which value(s) ofy maximizes Var(XIY = Y)?
1. A bad marksman takes 12 shots at a target with probability of hitting the target with each shot of 0.2, independent of other shots. Z is the random variable representing the number of hits. a. Calculate and plot the ...
6. 10 pts Use Laplace transforms to solve the damped spring-mass system xi’ +3×1 +2x = 0; x(0) = 1, 40) = —1.
5. a) find the Laplace transform of f(t)= { 21 1 < 3; , > 3. b) Find the inverse Laplace transform of F(s)== (s+V-i-4*
4. (a) [10 pt] Solve without Laplace transforms: y” —2y’ +5y = 0; y(0) = 1, y'(0) = 5. (b) 110 pt] Find the general solution of y” +4/ = 10ex.
3. Consider the differential equation —da = f(x) where f has the graph shown. dr (a) 15 pc) Determine the equilibrium solutions. (b) [5 pt] Which solutions in (a) are stable and which are unstable? (c) [5 ptj Sketch the ...