Suppose Y follows a Binomial(M,0.4) (a conditional Binomial distribution given M) and M follows a Poisson distribution with mean equal to 5, what is the unconditional distribution of Y? Suppose...
2. (a) Given that N-n, the conditional distribution of Y is x The unconditional distribution of N is Poisson (8). Calculate E(Y) and Var(Y). (b) A plant supervisor is interested in budgeting weekly repair costs for a certain type of machine. Records over the past years indicate that these repair cost have an exponential distribution with mean 20 for each machine studied. Let Y1, Y2, ..., Ysdenote the repair costs for five of these machines for the next week. Find...
5). Suppose that X2 Poisson co) and Ylx = x2 Binomial (X.P). a). Find the distribution of Y b). show that Y and x-y are incle Pendent
Question 14: Suppose that, conditional on N, X has a Binomial distribution with N trials and probability of success p, and that N, itself, is a Binomial distribution with m trials and probability of success r. Find b. The conditional distribution of given X-x.
Let X1, ... , Xn be iid with the Poisson(λ) distribution. What is the conditional distribution of Xi given the sample mean?
7. Suppose that waiting time, Y, at a particular restaurant follows an Exponential distribution with mean X, where X is a Geometric random variable with mean 1/ p. Find the unconditional mean and variance of Y.
Suppose that X 1 has a Poisson distribution with mean 2, X 2has a Poisson distribution with mean 3 , X 3 has a Poisson distribution with mean 5 and that X 1 , X 2 and X 3 are independent. Define Y = X 1 + X 2 + X 3. Determine the moment-generating function for Y.
Question 23 Suppose X has a Poisson distribution with a mean of 0.4. Determine the following probabilities. Round your answers to four decimal places (e.g. 98.7654) (a)P(X 2) (b)P(X S 5) (c)P(X-7) (d)P(X- 4)
6. (a) Given that X and Y are continuous random variables, prove from first principles that: (b) The random variable X has a gamma distribution with parameters-: 3 and A-2 . Y is a related variable with conditional mean and variance of =x)= Calculate the unconditional mean and standard deviation of Y. (c) Suppose that a random variable X has a standard normal distribution, and the conditional distribution of a Poisson random variable Y, given the value ol XOx, has...
Suppose X follows an exponential distribution with mean 7.5. Determine the conditional probability P(x > 2.5 I x ≤ 5).
24. Consider a binomial probability distribution with p=0.6, q=0.4 and n=15. The mean for this distribution is: a) 0.60 b) 0.90 c) 0.24 d) Neither of the above 25. Using the data in Question 24, what is the standard deviation of the distribution? a) 0.24 b) 73.6 c) VG d) ſ9 30. Consider a Poisson distribution with 2=9. The mean and standard deviation are: a) 3 and 9 b) 9 and 3 c) 9 and 9 d) None of the...