10. For a Poisson Random Variable (X) with a mean of 3.3; P(X>11) = ? a....
11. If the random variable X has a Poisson distribution such that P(X=1) = P(x=3), find P(X= 5). Give the answer with 6 dec. places
9. Let X be a Poisson random variable with parameter k = 3. (a) P[X 25] (b) Find P[5 S X <10) (c) Find the variance ? 10. Use the related Table to find the following: (here Z represents the standard normal variable) (a) P[Z > 2.57] (b) The point z such that PL-2 SZ sz]=0.8
Let X be a Poisson random variable with mean λ(a) Evaluate E{X(X −1)} from first principles, and from this, the variance of X. (b) Confirm the variance using the moment generating function of X.
Assume a random variable XX follows a Poisson distribution with a mean μ=3.7μ=3.7. Find P(X≤4) P(X≤4)=
The random variable X follows a Poisson process with the given value of lambda=0.11 and t=11 compute the following 1. P(4) 2. P(X<4) 3. P(X> or equal to 4) 4. P(3 < or equal to X < or equal to 7)
new random variable X is distributed as Poisson) in this question. We create a U where its probability mass function is P(X u) u) P(X 1) P(U for u = 1,2,... (a) Show that e P(U u)= 1- e-A u!' for u 1,2,. (6 marks) expression for the moment generating function of U (7 marks (b) Derive an (c) Find the mean and variance of U (7 marks) new random variable X is distributed as Poisson) in this question. We...
Question 3 Suppose that the random variable X has the Poisson distribution, with P (X0) 0.4. (a) Calculate the probability P (X <3) (b) Calculate the probability P (X-0| X <3) (c) Prove that Y X+1 does not have the Polsson distribution, by calculating P (Y0) Question 4 The random variable X is uniformly distributed on the interval (0, 2) and Y is exponentially distrib- uted with parameter λ (expected value 1 /2). Find the value of λ such that...
Random variable X is distributed Poisson, and P(X 2)-P(X 4). Find P(X 3)
Problem 6. [Poisson is Pronounced 'Pwah-ssohn] (a) Suppose that X is a random variable following the Poisson distribution with rate parameter A. Show that E[x]-A Hint: You may find the following fact useful: at k! (b) Suppose that we obtained the following count data: Count Frequency 24 30 17 19 Fit a Poisson distribution to the data using the Method of Moments (c) Suppose that X is a random variable that follows the Poisson distribution that you fit in part...
If X is a Poisson variable such that P(X=2)=3/10 and P(X=1)=1/5. Then P(0.2<X<2.9)+P(X=3.5) equal to A discrete random variable X has a cumulative distribution function defined by F(x) (x+k) for x = 0,1,2 Then the value of k is 16