Asked by Halima Soliman on May 09, 2024
Verified
The amount of money that Jon can save after working for a summer is a random variable S with a mean of μs\mu _ { \mathrm { s } }μs and a standard deviation of σs\sigma _ { s }σs .After saving this money Jon plans to go on a trip to India.He will change his money into Rupees at an exchange rate of 43 Rupees to one Dollar.This money he will bring to India.When he arrives in India he will buy a used motorbike.The price in India of a motorbike of the type he wants is a random variable B with a mean of μb\mu \mathrm { b }μb Rupees and a standard deviation of σb\sigma bσb Rupees. The amount of money Jon will have left (in Rupees) after changing his savings into Rupees and buying a motorbike in India is a random variable P which can be expressed in terms of S and B as P=43S−BP = 43 S - BP=43S−B Find expressions for the mean and variance of the random variable P.Assume that Jon's savings and the price of the bike are independent.
A) mean = 43 μs\mu _ { \mathrm { s } }μs - μb\mu \mathrm { b }μb ,variance = 1849 σs2\sigma _ { s } ^ { 2 }σs2 - σb2\sigma _ { b } ^ { 2 }σb2
B) mean = 43 μs\mu _ { \mathrm { s } }μs - μb\mu \mathrm { b }μb ,variance = 1849 σs2\sigma _ { s } ^ { 2 }σs2 + σb2\sigma _ { b } ^ { 2 }σb2
C) mean = 43 μs\mu _ { \mathrm { s } }μs + μb\mu \mathrm { b }μb ,variance = 1849 σs2\sigma _ { s } ^ { 2 }σs2 + σb2\sigma _ { b } ^ { 2 }σb2
D) mean = 43 μs\mu _ { \mathrm { s } }μs + μb\mu \mathrm { b }μb ,variance = 43 σs2\sigma _ { s } ^ { 2 }σs2 + σb2\sigma _ { b } ^ { 2 }σb2
E) mean = 43 μs\mu _ { \mathrm { s } }μs - μb\mu \mathrm { b }μb ,variance = 43 σs2\sigma _ { s } ^ { 2 }σs2 + σb2\sigma _ { b } ^ { 2 }σb2
Independent
A term used to describe two or more events that have no influence on each other's outcomes, or variables that do not show dependence.
Random Variable
A variable linked to the numerical results derived from unpredictable events.
Exchange Rate
The exchange rate is the value of one currency for the purpose of conversion to another, dictating how much one currency is worth in terms of another.
- Acquire knowledge of the mathematical manipulations and alterations executed on random variables.
- Comprehend the principles of mean and standard deviation within the realm of probability and statistics.
Verified Answer
Learning Objectives
- Acquire knowledge of the mathematical manipulations and alterations executed on random variables.
- Comprehend the principles of mean and standard deviation within the realm of probability and statistics.
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