Problem 3.026 The space shuttle flight control system called PASS (Primary Avion

Question

Problem 3.026 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 0.009. 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? Round all numbers to three decimal places (e.g. 98.765). Note: Use to indicate multiplication.

Explanation / Answer

This is a case of a Binomial distribution, so X here is a Binomial random variable.

Since the computers work in parallel, so this means that all computers vote independently.

The parameters for this distribution are:

n = 4, p = 0.009

Since X counts the number of computers that vote in the opposite direction roll, so it can take any values from 0 to 4.

Using the binomial pdf:

P(X=x) = nCx*(p^x)*((1-p)^(4-x))

So in this case we have:

P(X=x) = 4Cx*(0.009^x)*(0.991^(4-x))

We use this above formula to summarize the probability mass function for the Random variable:

P(X=0) = 4C0*(0.009^0)*(0.991^(4-0)) = 0.964

P(X=1) = 4C1*(0.009^1)*(0.991^(4-1)) = 0.035

P(X=2) = 4C2*(0.009^2)*(0.991^(4-2)) = 0.001

P(X=3) = 4C3*(0.009^3)*(0.991^(4-1)) = 0.0

P(X=4) = 4C1*(0.009^1)*(0.991^(4-1)) = 0.0

Thus we see that the probability of X having values 3 and 4 is almost equal to zero.

So the pdf is:

X    P(X) 0 0.964 1 0.035 2 0.001 3 0 4 0

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