The space shuttle flight control system called PASS (Primary Avionics Software Set) uses four independent computers working in parallel. At each critical step, the computers "vote" to determine the appropriate step. The probability that a computer will ask for a roll to the left when a roll to the right is appropriate is 0.0005. Let X denote the number of computers that vote for a left roll when a right roll is appropriate. Determine the cumulative distribution function of X.

Question

Susie Q

Mathematics

16 April, 01:15

The space shuttle flight control system called PASS (Primary Avionics Software Set) uses four independent computers working in parallel. At each critical step, the computers "vote" to determine the appropriate step. The probability that a computer will ask for a roll to the left when a roll to the right is appropriate is 0.0005. Let X denote the number of computers that vote for a left roll when a right roll is appropriate. Determine the cumulative distribution function of X.

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Answers (1)

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Heidi Arroyo · Answer 1

f (x) = P (X≤4) = 4Cx * 0.0005^x * 0.9995^ (4-x)

Step-by-step explanation:

Given

The range of values is given as {0,1,2,3,4}

Because any computer can fail.

Given that the failure of the computers are independent and

The probability of failure is given as 0.0005.

Cumulative Distribution Function is the the probability that a random variable is less than or equal to a specific value

So, we'll take the binomial effect into consideration.

It is given as

f (x) = P (X ≤ x) = 4Cx * 0.0005^x * (1 - 0.0005) ^ (4 - x)

f (x) = P (X≤4) = 4Cx * 0.0005^x * 0.9995^ (4-x)