a. Let X, X2,..., X, be i.i.d. random variables on the interval [0, 1] with pdf...

  
 

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a. Let X₁, X2,..., X, be i.i.d. random variables on the interval [0, 1] with pdf Г(3а) f(x) = 2-1 (1-2)²-1, a>0. T(a)T(2a) Find the method of moments estimator of a. b. The numbers w₁, 2,..., w, are known positive values. The random variables X₁, X2,..., X, are independent, and the distribution of X, is N1,). Both parameters and are unknown. Find the maximum likelihood estimates of u and o². Is û an efficient estimator of u? μ c. An electronic system consists of four components connected in series as shown in the figure below. The components function independently and each one has a lifetime (in weeks) that follows the exponential distribution with = Find the probability density function of the lifetime of this electronic system and use it to compute the system's expected lifetime. 20* A 0000 d. Refer to part (c). If the four components are connected in parallel as shown in the next figure, find the probability density function of the lifetime of this electronic system. A a. Let X₁, X2,..., X, be i.i.d. random variables on the interval [0, 1] with pdf Г(3а) f(x) = 2-1 (1-2)²-1, a>0. T(a)T(2a) Find the method of moments estimator of a. b. The numbers w₁, 2,..., w, are known positive values. The random variables X₁, X2,..., X, are independent, and the distribution of X, is N1,). Both parameters and are unknown. Find the maximum likelihood estimates of u and o². Is û an efficient estimator of u? μ c. An electronic system consists of four components connected in series as shown in the figure below. The components function independently and each one has a lifetime (in weeks) that follows the exponential distribution with = Find the probability density function of the lifetime of this electronic system and use it to compute the system's expected lifetime. 20* A 0000 d. Refer to part (c). If the four components are connected in parallel as shown in the next figure, find the probability density function of the lifetime of this electronic system. A

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Question a is missing but we can still go through question b c and d Lets start with question b b The random variables X1 X2 Xn are known positive values The distribution of Xi is N vi where both para... View the full answer