Question

The space shuttle flight control system uses four independent, parallel computers. At each critical step, the computers "vote" to determine the appropriate step, for instance, firing the control thrusters to roll the shuttle to the left. The system has been designed such that the probability' that a single computer will ask for a roll to the left when a roll to the right is appropriate is 0.0001. Let X denote the number of computers that "vote" for a left roll when instead a right roll is appropriate. Find the probability mass function of X. (You will need to establish the sample space of X (the possible outcomes of X).)

Answer 1

The probability mass function (PMF) of X, the number of computers that 'vote' for a left roll when a right roll is appropriate, can be determined using the binomial distribution formula. The PMF of X can be calculated for values ranging from 0 to 4, based on the probabilities of each outcome.

Step-by-step explanation:

The probability mass function (PMF) of X, the number of computers that 'vote' for a left roll when a right roll is appropriate, can be determined by considering the possible outcomes of X. Since there are four independent computers, X can take on values from 0 to 4. The PMF of X can be calculated using the binomial distribution formula:

P(X=k) = C(4,k) * (0.0001)^k * (1 - 0.0001)^(4-k)

where C(4,k) is the number of combinations of choosing k out of 4. The PMF of X is:

1. P(X=0) = C(4,0) * (0.0001)^0 * (1 - 0.0001)^(4-0)
2. P(X=1) = C(4,1) * (0.0001)^1 * (1 - 0.0001)^(4-1)
3. P(X=2) = C(4,2) * (0.0001)^2 * (1 - 0.0001)^(4-2)
4. P(X=3) = C(4,3) * (0.0001)^3 * (1 - 0.0001)^(4-3)
5. P(X=4) = C(4,4) * (0.0001)^4 * (1 - 0.0001)^(4-4)

By substituting the values into the formula, we can calculate the probabilities of each outcome.