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Let X be the time it takes for a person to choose a birthday gift, where X has an average value of 27 minutes. If the random variable X is known to be exponentially distributed, what are the parameters of this exponential distribution

User Guy Dafny
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6 votes

Answer:

The parameters of this exponential distribution is
\lambda =
(1)/(27) .

Explanation:

We are given that the random variable X is known to be exponentially distributed and let X be the time it takes for a person to choose a birthday gift, where X has an average value of 27 minutes.

So, X = time it takes for a person to choose a birthday gift

The probability distribution function of exponential distribution is given by;


f(x) = \lambda e^(-\lambda x) , x >0 where,
\lambda = parameter of distribution.

Now, the mean of exponential distribution is =
(1)/(\lambda) which is given to us as average value of 27 minutes that means
\lambda = (1)/(27) .

So, X ~ Exp(
\lambda = (1)/(27) ) .

Therefore, the parameter of this exponential distribution is
\lambda .

User Harshith Thota
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