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Possible values of X, the number of components in a system submitted for repair that must be replaced, are 1, 2, 3, and 4 with corresponding probabilities .15, .35, .35, and .15, respectively. a. Calculate E(X) and then E(5 2 X). b. Would the repair facility be better off charging a flat fee of $75 or else the amount $[150/(5 2 X)]

Answer :

Answer:

Step-by-step explanation:

Given that possible values of X, the number of components in a system submitted for repair that must be replaced, are 1, 2, 3, and 4 with corresponding probabilities .15, .35, .35, and .15, respectively

To find E(x)

[tex]E(x) = \Sigma x_i p_i\\= 1(0.15)+2(0.35)+3(0.35)+4(0.15)\\=0.15+0.70+1.05+0.60\\= 2.50[/tex]

To find E(5.2x)

By linear property ofExpectation we have

E(5.2x) = [tex]5.2E(x) \\=5.2*2.5\\=13[/tex]

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Flat fee of 75 would incur a cost of 75*2.5 = 187.50

Instead 150 (5.2x) would incur on an average = 150

The second one is preferred as it shows cost to be lower.

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