Problem 7 (9 pts) Suppose X follows Chi-square distribution with $\nu = 6$ (a) (3 pts) Write down the pdf of X, remember to include the support. (b) (3 pts) Calculate Var(100X - 200). (c) (3 pts) Calculate P(X $\ge$ 10). (Hint: Chi-square distribution is a special case of some other distributions)
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Step 1: The probability density function (pdf) of a chi-square distribution with v degrees of freedom is given by: $$f(x) = \frac{1}{2^{v/2} \Gamma(v/2)} x^{v/2-1} e^{-x/2}$$ where x > 0 and Γ(v/2) is the gamma function. Show more…
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