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I. Find E(T) for a component that reliability function R(t) = pe-At, t > 0,0 <...
2. If a random variable T has failure rate function h(t) - a + bt,t > 0, find the pdf and reliability function ofT
4 Suppose f : (0,0) → (0,x), is a differentiable function satisfying f(a +b)-f(a)fb), for all a,b>0 Moreover, assume that f(0)1 (a) Prove that there exists λ (not necessarily positive) such that f(r) = e-Ar, for all r. Hint Find and solve a proper differential equation. (b) Suppose that X is a continuous random variable, with P(X>ab)-P(>a)P(X> b), for all a, b e (0, oo). Prove that X is exponentially distributed
The probability mass function of a random variable X is given by Px(n)r n- (a) Find c (Hint: use the relationship that Ση_0 n-e) (b) Now assume λ = 2, find P(X = 0) (c) Find P(X>3)
Find the normal component of acceleration for r(t) = e' cost i + e' sintj+e' k. Give an exact answer. The graph is shown here: 2 0.0 0.5 0 1.0 1.5 Find the normal component of acceleration for r(t) = e' cost i + e' sintj+e' k. Give an exact answer. The graph is shown here: 2 0.0 0.5 0 1.0 1.5
4.3 Calculate the reliability of the system in Figure 4.35, where component i has reliability R (i-1,2,..., 8). 4 FIGURE 4.35 Reliability block diagram of Problem 4.3 4.3 Calculate the reliability of the system in Figure 4.35, where component i has reliability R (i-1,2,..., 8). 4 FIGURE 4.35 Reliability block diagram of Problem 4.3
Find the MME for r and λ for the Gamma distribution given by fX(x; r, λ) = λ r Γ(r) x r−1 e −λx where x > 0, r > 0, and λ > 0. Assume a random sample of size n has been drawn ar-le-k 4. Find the MME for r and λ for the Gamma distribution given by fx(z;r, A) where x > 0, r > 0, and λ 〉 0, Assume a random sample of size n...
4. Let y1θ ~iid Uniform (0,0), for i-1, n, Assume the prior distribution for θ to , be Pareto(a, b), where p()b1 for 0> a and 0 otherwise. Find the posterior distribution of θ.
I. (5 points) Let X be a random variable with moment generating function M(t) = E [etx]. For t > 0 and a 〉 0, prove that and consequently, P(X > a inf etaM(t). t>0 These bounds are known as Chernoff's bounds. (Hint: Define Z etX and use Markov inequality.)
I need the formula four component reliability when strength is exponentially distributed and stress is normally distributed. please drive this formula and show the steps so I may apply it. here are the formulas for exponential strength denoted by G and normal stress denoted by s. what is the formula for component reliability for when the strength function is exponentially distributed and the stress function has a normal distribution. the answer should be equal to Rc=.6096( this is what our...
Solve the heat flow problem 5 t>0,0<<7, (0,t) = 0, t>0, Od (1, t) = 0, +>0, u(2,0) = 1+cos I, 0<<1. Find lim 100 u(2,t).