Let X and Y be independent gamma random variables, both with the same scale parameter ß. The value..
Let X and Y be independent gamma random variables, both with the same scale parameter β. The value of the shape parameter is α1 for X and α2 for Y. Use moment generating functions to show that X + Y is also gamma distributed, with shape parameter α1 + α2 and scale parameter β. Is X + Y gamma distributed if the scale parameters are different? Explain.Let X and Y be independent rvs, with X ~ N(0, 1) and Y ~ N(0, 1). (a) Use convolution to show that X+Y is also normal, and identify its mean and standard deviation. (b) Use the additive property of the normal distribution presented in this section to verify your answer to part (a).Refer to Exercise 3. Apr 08 2022 03:22 PM
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