There is poisson random variable X with T*lambda_MUE.
There is poisson random variable Z with lambda_SMC.
And i define new random variable K=aX+bZ. (a and b is positive integer which is greater than 0)
To calculate pmf of K i used conv function.
And calculate using below command but it is not equal to E[K]
What i expect is 123 but result is 43 .
What is wrong?
Thank you
lambda_MUE = 2;lambda_SMC = 3;alpha = 3; beta = 1; T=20; g=alpha*(0:1:110);z=beta*(0:1:110);K=0:1:(max(g)+max(z));P_X = ((T*lambda_MUE).^(g/alpha))./(factorial(g./alpha)).*exp(-T*lambda_MUE);P_Z = (lambda_SMC.^(z./beta))./(factorial(z./beta)).*exp(-lambda_SMC);P_K = conv(P_X,P_Z);sum(K(1:1:length(P_K)).*P_K)
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