(b) Assume that \( X \) is a geometric random variable with \( p = 0.2 \). Compute \( E[(X - 5)^2] \). This does not require a messy calculation!(i) 10(ii) 15(iii) 20(iv) 25 **Instructions**Complete the following multiple choice questions. No work will be graded in the bonus problem.**(a)** Assume that \( X \) is a random variable with \( E(X) = -3 \) and \( E(X^2) = 16 \). Compute \( E[-X(3X - 2)] \).(i) \(-54\) (ii) \(-48\) (iii) \(-33\) (iv) \(-27\)

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Answered: Complete the following multiple choice…

A First Course in Probability (10th Edition)

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ISBN:9780134753119

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Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Q7. Let X; (i = 1,.,n) be a random sample from the N(u, o²) population with unknown parameters u and o?. Then we know that T, = E-1(X - X)²/(n – 1) is an unbiased estimator -xi-1 . Now consider two other estimators T, and T3 for o? where of a? and further, (n-1)T T2 = E(X – X)*/n and T3 = E(X – X)²/n + 1). %3D What is the variance of T,? Find out the variances and biases of T2 and T3 and thus obtain their m.s.e.'s. Show that among the three estimators T,, T2 and T3 the one with minimum m.s.e. is T3.
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Complete the following multiple choice questions. No work will be graded in the bonus problem. (а) E(X²) = 16. Compute E[-X(3X – 2)]. Assume that X is a random variable with E(X) = -3 and (i) -54 (ii) -48 (iii) 33 (iv) -27