Let ๐‘‹ be a random variable exponentially distributed with parameter ๐œ† > 0.โ€ฆ

Let ๐‘‹ be a random variable exponentially distributed with parameter ๐œ† > 0. The probability density function of X is given by:

fX(x)={ฮปeโˆ’ฮปx,ifย xโ‰ฅ00,otherwisef_X(x) = \begin{cases} \lambda e^{-\lambda x}, & \text{if } x \geq 0 \\ 0, & \text{otherwise} \end{cases}

If 5๐ธ(๐‘‹) = ๐‘‰๐‘Ž๐‘Ÿ(๐‘‹), where ๐ธ(๐‘‹) and ๐‘‰๐‘Ž๐‘Ÿ(๐‘‹) indicate the expectation and variance of ๐‘‹, respectively, the value of ๐œ† is ______ (rounded off to one decimal place).

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