Context for question 4The random variables D and E have the independent distributions D∼Po(1.7) and E∼Po(2.1).
4(a)Poisson DistributionMedium3 marksFind P(D+E<4).Show your methodTypeWriteMath0 wordsProbabilityGrade answerSolutionGrading criteria
4(b)Poisson DistributionMedium3 marksGiven that D+E<4, find P(D=1).Show your methodTypeWriteMath0 wordsProbabilityGrade answerSolutionGrading criteria
4(c)Normal Distribution Normal ApproximationsHard4 marksThe random variable T is the total of 100 randomly chosen values of D. Use the normal approximation to the Poisson distribution to find P(T>190).Show your methodTypeWriteMath0 wordsProbabilityGrade answerSolutionGrading criteria