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Let X And Y Be Independent Discrete Random Variables With The Following PDFs: X 0 1 2 F(x)=P[X=x] 0.

Let X and Y be independent discrete random variables with the following PDFs:

x | 0 | 1 | 2 |

f(x)=P[X=x] | 0.5 | 0.3 | 0.2 |

y | 0 | 1 | 2 |

g(y)= P[Y=y] | 0.65 | 0.25 | 0.1 |

(a) Show work to find the PDF h(w) = P[W=w] = (f*g)(w) (the convolution) of W = X + Y

(b) Show work to find E[X], E[Y] and E[W] (note that E[W] = E[X]+E[Y])