Extra Credit Question:[4+4=8 pts) If E [exp(aX)] exists for a given constant a, then show that...
Extra Credit Question:[4+4=8 pts) If E [exp(aX)] exists for a given constant a, then show that for to (a) exp(-at)P(x >t) <E (exp(aX)], if a > 0. (b) exp(-at)P(X <t) <E (exp(aX)], if a < 0.
If E [exp(aX)] exists for a given constant a, then show that for t > 0 (a) exp(−at)P (X > t) < E [exp(aX )] , if a > 0. (b) exp(−at)P (X < t) < E [exp(aX )] , if a < 0.
For the Weibull distribution with parameters a and \, recall that for t > 0 the density function and distribution function are, respectively, f(t) = alºja-1e-(At)a F(t) =1-e-(At)a Suppose that T has the Weibull distribution with parameters a = 1/2 and 1 = 9. an (4 points) Compute work. approximation of P(1 < T < 1.01 T > 1) using the hazard rate. Show y
Please show all work.
1. For the circuit shown in Figure 1 below, find the equation for ve(t) for t> 0. Extra Credit: Find the time constant ( 1 ) and indicate how long it will take to fully discharge the capacitor voltage. Hint: You have to draw the following circuits at: t=0-, t=0+, RTH too 2 t 3r Velt) :4 9A 5F Figure 1.
1. Given a continuous random number x, with the probability density P(x) = A exp(-2x) for all x > 0, find the value of A and the probability that x > 1.
2) Sketch the phase portrait of the system x' (t) = Ax (t) if (a) 5= [ 9), P=[7"}] (1) 5= [ • ? ], P=[} >>]
Could someone explain how these to get these phase portraits by
hand with ẋ=y and ẏ=ax-x^2 especially for a=0 case where you have
eigenvalues all equal to zero?
6.5.4 a>0 Sketch the phase portrait for the system x = ax-x, for a < 0, a = 0, and For a -(0 We were unable to transcribe this imageFor a>0 ES CS
1. For the circuit shown in Figure 1 below, find the equation for ve(t) for t> 0. Extra Credit: Find the time constant ( 1 ) and indicate how long it will take to fully discharge the capacitor voltage. Hint: You have to draw the following circuits at: t=0-, t=0+, RTH too 2 + 3r Velt) :4 9A 5F Figure 1.
8. Consider ar? +5 I <3 f(0) = 12.c +b > 3 Determine a and b such that f is continuous and differentiable at x = 3. )={
4. (a) Suppose that limz-c f(x) = L > 0. Prove that there exists a 8 >0 such that if 0 < 12 – c < 8, then f(x) > 0. (b) Use Part (a) and the Heine-Borel Theorem to prove that if is continuous on (a, b) and f(x) > 0 for all x € (a, b), then there exists an e > 0 such that f(x) > € for all x € [a, b].