please answer 3). Assume two random variables X and Y both follow the binomial distribution Bin(n,...

Question

Question

please answer
3). Assume two random variables X and Y both follow the binomial distribution Bin(n, p). Does X+Y also follow a binomial dist

math Advanced-Math

Answer 1

Answer #1

Sol? Let, xorn Bin (0, p) Now let ockcan then IP (X+Y= k) = Z IP ( X = ? , Y = 6-1) 19(x-1) (Y= 6-i) (ny independenre) - ( )

Answer 2

Similar Homework Help Questions

Let X, Y be independent random variables where X is binomial(n = 4, p = 1/3)...

Let X, Y be independent random variables where X is binomial(n = 4, p = 1/3) and Y is binomial(n = 3,p = 1/3). Find the moment-generating functions of the three random variables X, Y and X + Y . (You may look up the first two. The third follows from the first two and the behavior of moment-generating functions.) Now use the moment-generating function of X + Y to find the distribution of X + Y .
(4) Suppose that {X;}-1 iid random variables from a Binomial distribution Bin(m, p). Using your answer...

(4) Suppose that {X;}-1 iid random variables from a Binomial distribution Bin(m, p). Using your answer in (3) obtain an approximate 99% confidence interval for the pa- rameter p based on the MLE. Explain how you would estimate the Fisher information matrix.
Suppose that we have two independent binomial random variables X ~Binomial(n, px) and Y ~ Binomial(m,Pv)....

Suppose that we have two independent binomial random variables X ~Binomial(n, px) and Y ~ Binomial(m,Pv). You can assume that the MLE's are -X/n and p,-Y/m. (a) Find the MLE for p under the assumption that p (b) Find the LRT statistic T for testing p,-py HA:p.Ру vs. (c) Evaluate the value of this statistic if n 353, X 95, m -432, and Y 123. (d) Compare the answer from part (c) to a critical value from a x2 with...

Let X and Y be two random variables. We assume that Y has a Gamma distribution...

Let X and Y be two random variables. We assume that Y has a Gamma distribution with parameters ? and ? and that the conditional distribution of X, given Y=y is a Poison distribution with discrete probability function, ??|?(?|?)=?^(−?)^(?^?)/?!, ?=0,1,2,…. a. Show that X has a negative binomial distribution
Let X and Y be independent binomial random variables B(n,p) on the same sample space. Show that X + Y is also a binomial...

Let X and Y be independent binomial random variables B(n,p) on the same sample space. Show that X + Y is also a binomial random variable B(?,?). What values should replace the questions marks?
Assume that and Z2 are two independent random variables that follow the standard normal distribution N(0,1),...

Assume that and Z2 are two independent random variables that follow the standard normal distribution N(0,1), so that each of them has the density º(z) = -20 <z<00. Let X = vz1 + Z2, Y = y21 - vž Z2, S = x2 + y2, and R= . (e) From (c), please find the densities of X2 and Y?. (f) From (d) and (e), please find the density of x2 + y2(=S). (g) From (e), please find the density of...

yes 5. Let X and Y be two random variables which follow standard normal distribution. Let...

yes 5. Let X and Y be two random variables which follow standard normal distribution. Let U = X - Y. Find the distribution function of U. Also find E[U] and Var[U).
Assume that 2 and Z, are two independent random variables that follow the standard normal distribution N(0,1), so that...

Assume that 2 and Z, are two independent random variables that follow the standard normal distribution N(0,1), so that each of them has the density - . - < < . Let X = 22 + 2 Z2, Y = 22 - Z2, S = x2 +Y, and R = xy (e) From (c), please find the densities of X? and Y? (f) From (d) and (e), please find the density of X2 +Y? (=S). (g) From (e), please find...
Assume that Z1 and 22 are two independent random variables that follow the standard normal distribution...

Assume that Z1 and 22 are two independent random variables that follow the standard normal distribution N(0,1), so that each of them has the density 0(3) = , Let X = {{z + 12 Zz, Y = 122- x2z2, S = x2 + y2, and R= * Answers, a,b,c,d,e are provided below need help with g, hi (g) From (e), please find the density of (X,Y) (note that X2 and Y2 are independent from (a)). (h) From (g), please find...

please help with both ***Assume that a procedure yields a binomial distribution with a trial repeated...

please help with both ***Assume that a procedure yields a binomial distribution with a trial repeated n = 16 times. Find the probability of X > 3 successes given the probability p = 0.26 of success on a single trial. (Report answer accurate to 3 decimal places.) ***Assume that a procedure yields a binomial distribution with a trial repeated n=20n=20 times. Find the probability of x≥11x≥11 successes given the probability p=0.6p=0.6 of success on a single trial. (Report answer accurate...