**Problem 4.144**Consider a random variable \( Y \) with density function given by:\[f(y) = k e^{-y^2/2}, \quad -\infty < y < \infty.\]a. Find \( k \).b. Find the moment-generating function of \( Y \).c. Find \( E(Y) \) and \( V(Y) \).

a) The integral of the density function over its entire range must equal 1 since the total…

Answered: 4.144 Consider a random variable Y with…

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4.144 Consider a random variable Y with density function given by f(y)=ke-²/2 a Find k. b Find the moment-generating function of Y. c Find E(Y) and V (Y). -∞