3. A random variable X takes values between -2 and 3 with a probability density function f(x) = { 15/64 + x/64, if -2 ? x ? 0 3/8 + cx, if 0 < x ? 3 0, elsewhere } (a) Find the value of c and sketch the probability density function. (b) FIND P(-1 ? X ? 1), (c) Find and DRAW cumulative distribution function. (d) FIND E(X) and V(X).
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Since f(x) is a probability density function, we know that the integral of f(x) over its entire range must equal 1. So, we have: $$\int_{-2}^0 s\cdot x\, dx + \int_0^3 0\, dx = 1$$ Show more…
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