# (a) X is a Random variable with mean = mu. What would be the new value of the mean if each value...

## Question:

(a) X is a Random variable with mean = {eq}\mu {/eq}. What would be the new value of the mean if each value of x was increased by 3?

(b) X is a random variable with {eq}\mu {/eq} = E(x) = 14.2. Calculate 2E(x + 3)

(c) X is a random variable with standard deviation {eq}\sigma {/eq}. If each value of x is transformed to 5x, what is the standard deviation of the new distribution?

## Mean and Standard Deviation:

The expected value or the mean of a constant term is that constant term itself. While the standard deviation or the variance of a constant term is zero. As variance or the standard deviation represents the variation in the data set if the term is constant i.e. no variation then the standard deviation is zero.

## Answer and Explanation:

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(a) The mean of x {eq}= \mu {/eq}

If each value of x was increased by 3 then mean will also increase by 3 i.e. the new mean value of the x is equal...

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#### Learn more about this topic: Evaluating the Expected Value of Sample Information

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Chapter 5 / Lesson 10
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Many companies consider doing surveys and market research but are not sure whether the expense is worth the data that will be collected. This lesson helps explain how to calculate the expected value of sample information.