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In: Statistics and Probability

A random variable X is Normally distributed with mean = 75 and = 8. Let Y...

A random variable X is Normally distributed with mean = 75 and = 8. Let Y be a second Normally distributed random variable with mean = 70 and = 12. It is also known that X and Y are independent of one another. Let W be a random variable that is the difference between X and Y (i.e., W = X – Y). What can be said about the distribution of W?

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Expert Solution

Random variable X is normally distributed with mean = 75 and variance = 8.

Therefore, X Normal (75, 8)

Random variable Y is normally distributed with mean = 70 and variance = 12.

Therefore, Y Normal (70, 12)

It is known that X and Y are independent of one another.

Let W be a random variable that is the difference between X and Y

Therefore, W = X - Y

According to the properties of the normal distribution, the distribution of the difference of two normally distributed independent random variables A and B with mean and variances (a, a2) and (b, b2) respectively is also normally distributed with mean and variances (a - b, a2 + b2)

Therefore, W is normally distributed with mean = 75 - 70 = 5 and variance = 8 + 12 = 20

W Normal (5, 20)

orchestra answered 3 years ago
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