2. A continuous random variable X has probability density function: (f(x) = egin{cases} kx & 0 < x < 2 \ 0 & ext{otherwise} end{cases}) a. Find the constant k so that f is a valid pdf. b. Find P(X<1). c. Find the cumulative distribution function, F(x) (don't forget bounds!).
Added by Montserrat A.
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Step 1
For a function to be a valid probability density function (pdf), the integral of the function over its entire range must equal 1. In this case, the range of X is from 0 to 2. So, we need to solve the following equation for k: ∫ from 0 to 2 of kx dx = 1 This Show more…
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