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scZoUnD [109]
3 years ago
9

The space shuttle flight control system called PASS (Primary Avionics Software Set) uses four independent computers working in p

arallel. 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 0.003. Let X denote the number of computers that vote for a left roll when a right roll is appropriate. What is the probability mass function of X
Mathematics
1 answer:
tigry1 [53]3 years ago
6 0

Answer:

f_X(k)=\binom{4}{k}0.003^k0.997^{4-k}

Step-by-step explanation:

Recall that a <em>probability mass function</em> defined on a discrete random variable X is just a function that gives the probability that the random variable equals a certain value k

f_X(k)=P(X=k)

In this case we have the event  

“The computer will ask for a roll to the left when a roll to the right is appropriate” with a probability of 0.003.

Then we have 2 possible events, either the computer is right or not.

Since we have 4 computers in parallel, the situation could be modeled with a binomial distribution and the probability mass function

f_X(k)=\binom{4}{k}0.003^k0.997^{4-k}

This gives the probability that k computers are wrong at the same time.

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