[Steps Shown] A random variable X follows a distribution with probability density function f_X(x)=k e^-x, 0 ≤q x Determine the value of k. (6 points)
Question: A random variable \(X\) follows a distribution with probability density function
\[f_{X}(x)=k e^{-x}, \quad 0 \leq x<\infty .\]- Determine the value of \(k\). (6 points)
- Calculate the cumulative density function \((\mathrm{cdf}), F(0.2) .(6\) points)
- A median of a distribution is defined as a value m such that \(\int_{-\infty}^{m} f_{X}(x) d x=\int_{m}^{-\infty} f_{X}(x) d x=1 / 2\). Find the median of \(X\).
Deliverable: Word Document 
![[Steps Shown] Suppose X follows a distribution](/images/solutions/MC-solution-library-66123.jpg "[Steps Shown] Suppose X follows a distribution with the density")
[Steps Shown] Suppose X follows a distribution with the density
(Steps Shown) The amount (unit: ounce) of fill dispensed by a bottle
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[Solution Library] Compute the following limits or argue that they do
(Step-by-Step) Consider the integral ∫_0^1 ∫_1^e^x d y d
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[See Steps] Compute the integral ∫_0^2 ∫_0^√4-y^2
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