The weekly downtime Y (in hours) for a certain instrument of a company has approximately

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answerhappygod
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The weekly downtime Y (in hours) for a certain instrument of a company has approximately

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The weekly downtime Y (in hours) for a certain instrument of a company has approximately a gamma distribution with a = 3 and ß = 2. The loss in OMR to the company as a result of downtime is given by L = 30Y + 2Y2. What is the expected value of L. (a) 276 (b) 456 (0) 385 (d) 367




Correct option:

(a) 276

Explanation:

Mean of Gamma Distribution = E(Y) = аз = 3 X 2 = 6

Variance of Gamma Distribution = \sigma ^{2} = a 32 = 3 x 22 = 12

We have:

o2 = E(Y) – (E(Y))

Substituting values, we get:

12 = E(Y?) - 64

So, we get:

E(Y? = 36 + 12 = 48

Given:

L = 30Y + 2Y

So, we get:

E(L) = (30 x E(Y)] + [2 x E(Y?)

Substituting values, we get:

E(L) = (30 x 6] + 2 x 48

= 180 + 96

= 276
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