The number of years a radio function is exponentially distributed with parameter λ = 3/8. If...

The number of years a radio function is exponentially distributed with parameter λ = 3/8. If Jonas buys a used radio, what is the probability that it will be working after an additional 8 years, if
(a) the radio is at least 3 years old? You are encouraged to use MATLAB for calculation.
(b) the radio is at least 10 years old? You are encouraged to use MATLAB for calculation.

Solutions

Expert Solution

let X be number of years a radio function, which is exponentially distributed with parameter λ = 3/8.

So,

a) Probability that it will be working after an additional 8 years, if the radio is at least 3 years old

for a exponential random variable, with rate parameter ,

So,

So, here, , so.

Hence,

b) The above one was the method, in which you would solve normally. Now, we'll solve the next one using 'memoryless property of exponential distribution'.

According to memory less property,

probability that it will be working after an additional 8 years, if the radio is at least 3 years old

We see that both the probabilities are equal since, it doesn't depend on how many years it has been previously used.

[If you need the matlab commands for this, please comment, I'll add it to the answer]

orchestra answered 1 year ago

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