If X1 and X2 are independent random variables having binomial distributions with the respective parameters n1 and θ and n2 and θ, show that Y = X1 + X2 has the binomial distribution with the parameters n1 + n2 and θ.
Answer to relevant QuestionsIf X1 and X2 are independent random variables having the geometric distribution with the parameter θ, show that Y = X1 + X2 is a random variable having the negative binomial distribution with the parameters θ and k = 2. Consider two random variables X and Y whose joint probability density is given by Find the probability density of U = Y – X by using Theorem 7.1 as modified on page 216. In example 7.13 we found the probability destiny of the sum of two independent random variables having the uniform destiny with α = 0, and β = 1. Given a third random variable X3, which has the same uniform destiny and is ...With reference to Exercise 3.93 on page 107, find the probability density of the average mileage of two such tires. Assume independence. Use a computer program to generate 10 “ pseudorandom” numbers having the standard normal distribution.
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