Refer to Exercise 5.43. Assume that the number of breakdowns on different days are independent of one
Question:
Refer to Exercise 5.43. Assume that the number of breakdowns on different days are independent of one another. Let X and Y denote the number of breakdowns on each of two consecutive days.
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a. Complete the preceding joint probability distribution table.
P({X = 0} & {Y = 2}) = P(X = 0) · P(Y = 2)
= 0.80 · 0.05 = 0.04.
b. Use the joint probability distribution you obtained in part (a) to determine the probability distribution of the random variable X + Y, the total number of breakdowns in two days; that is, complete the following table.
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c. Use part (b) to find μX+Y and σ2X+Y.
d. Use part (c) to verify that the following equations hold for this example:
μX+Y = μX + μY
and
-3.png)
The mean and variance of X and Y are the same as that of W in Exercise 5.43.
e. The equations in part (d) hold in general: If X and Y are any two random variables,
μX+Y = μX + μY.
In addition, if X and Y are independent,
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Interpret these two equations in words.
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a b Columns 1 and 2 of the preceding table comprise the probability distribution o...View the full answer
