Let X have an exponential distribution with parameter > 0. Find p P[k < X < k +1] = p(1 − p)k . such that
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Let X have an exponential distribution with parameter 2 > 0. Find
P[k < X < k + 1] = p(1 − p)k .
such that](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faa691764-c764-4f75-bf7f-441acd22bffa%2F07281353-afce-4c62-b818-b21dbc63ebaf%2Fj44my6d_processed.png&w=3840&q=75)
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- Recall that the general form of a logistic equation for a population is given by P(t)=c1+aebt , such that the initial population at time t=0 is P(0)=P0. Show algebraically that cP(t)P(t)=cP0P0ebt .LetX1,X2,...,Xn be a sequence of independent and identically distributed random variables having the Exponential(λ) distribution,λ >0, fXi(x) ={λe−λx, x >0 0, otherwise Define the random variable Y=X1+X2+···+Xn. Find E(Y),Var(Y)and the moment generating function ofY.LetX1,X2,...,Xn be a sequence of independent and identically distributed random variables having the Exponential(λ) distribution,λ >0, fXi(x) ={λe−λx, x >0 0, otherwise (a) Show that the moment generating function mX(s) :=E(esX) =λ/(λ−s) for s< λ;
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