# Question: Suppose a random variable X has a PDF which is

Suppose a random variable X has a PDF which is nonzero only on the interval [ 0, 8 ) . That is, the random variable cannot take on negative values. Prove that

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A random variable X has a characteristic function, ϕX (ω). Write the characteristic function of Y= aX+ b in terms of ϕX (ω) and the constants a and b. A Cauchy random variable has a PDF (a) Find the characteristic function, ϕX(ω) . (b) Show that the derivatives dk / dωk (ϕX(ω)) do not exist at ω = 0.What does this mean? For a Poisson random variable whose PMF is given by Find the following: (a) The probability- generating function, HX( z) , (b) The Taylor series expansion of HX( z) about the point z = 1 , (c) A general expression for the ...Consider a moment- generating function of the general form For constants a, b, and c. Find constraints that the constants a, b, and c must satisfy so that MX (u) is the MGF of a valid random variable. In an expression was derived for E [euX2] for a Rician random variable. Use this function to obtain a saddle point approximation for the tail probability of a Rician random variable, Pr (X ≥ xo). For one- sided random ...Post your question