Mean Without Failure Rate For Exponential Distribution

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Suppose X is an exponential random variable with P(X<4.19)=0.632

How do I find the mean of X with just this information?

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Hints:

  • $F_X(x)=1-e^{-\lambda x}$ and the equality in your question enables you to find $\lambda$.

  • $\mathbb EX=\frac1{\lambda}$