Assume That $\mathrm { x }$ Is a Random Variable in a Probability Distribution with Mean

question 89

Multiple Choice

Assume that $\mathrm { x }$ is a random variable in a probability distribution with mean $\mu$ and standard deviation $\sigma$ . Find expressions for the mean and standard deviation if every value of $\mathrm { x }$ is modified by first being multiplied by 5 , then increased by 4 .

• A) \(\mu _ { \text {new } } = 5 \mu + 4 ; \sigma _ { \text {new } } = 5 \sigma + 4\)
• B) \(\mu _ { \text {new } } = 4 \mu + 5 ; \sigma _ { \text {new } } = 4 \sigma\)
• C) \(\mu _ { \text {new } } = \mu + 4 ; \sigma _ { \text {new } } = 5 \sigma\)
• D) \(\mu _ { \text {new } } = 5 \mu + 4 ; \sigma _ { \text {new } } = 5 \sigma\)

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Definitions:

Default

Failing to fulfill a legal obligation or agreement, particularly the failure to repay a loan as agreed with a lender.

Perfection

In legal and financial terminology, it refers to the necessary steps taken to secure rights or interests in collateral against third parties.

Security Interest

A legal claim or lien on collateral, giving a lender the right to take property to satisfy a debt if the debtor defaults.

Default

The failure to meet the legal obligations of a loan, typically by not making the required payments.