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SOLVED:[M] Mean and variance for the normal distribution. Consider a normally distributed variable Y with density f given in (4.1); that is, f(y)=(1)/(√(2 πσ^2)) (-(1)/(2 σ^2)(y-μ)^2), -∞<y<∞The expected value or mean of Y is defined as the average value where each possible value y between -∞and ∞is assigned the weight f(y) : E(Y)=∫-∞^∞ y f(y) d y 1. Show that ∫-∞^∞(y-μ) f(y) d y=0. [Hint: Use a substitution v=y-μand the fact that f is symmetric around μ.] 2. Show that E(Y)=μ. The variance of
SOLVED:[M] Mean and variance for the normal distribution. Consider …
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