Show that the binomial probability function is unimodal in x (i.e., p(x) either always increases in x; or only decreases in x; or increases to a maximum and then decreases as x goes from 0 to n). Hint: Consider p(x)/p(x-1).
Show that the binomial probability function is unimodal in x (i.e., p(x) either always increases in...
Show that if X follows a binomial distribution with n, trials and probability of success p,-p,jz 1,2, Hint: Use the moment generating function of Bernoulli random variable) 1. , n and X, are independent then X, follows a binomial distribution.
4-3) The function (x) xe is unimodal with maximum at x-1 as the figure below. 5 as a form of . Use this fact to define the critical region of the likelihood Express ratio test, whose form is de fined as k, 0<k<1 [Hint] c1. cO or (n-1)S/o From the graph, 2sk implies (n-1)S2/o
4-3) The function (x) xe is unimodal with maximum at x-1 as the figure below. 5 as a form of . Use this fact to define...
Calculate the following binomial probability by either using one of the binomial probability tables, software, or a calculator using the formula below. Round your answer to 3 decimal places. P(x | n, p) = n! (n − x)! x! · px · qn − x where q = 1 − p P(x = 11, n = 13, p = 0.70) =
Calculate the following binomial probability by either using one of the binomial probability tables, software, or a calculator using the formula below. Round your answer to 3 decimal places. P(x | n, p) = n! (n − x)! x! · px · qn − x where q = 1 − p P(x > 12, n = 15, p = 0.7) =
Calculate the following binomial probability by either using one of the binomial probability tables, software, or a calculator using the formula below. Round your answer to 3 decimal places. P(x | n, p) = n! (n − x)! x! · px · qn − x where q = 1 − p P(x = 10, n = 12, p = 0.75) =
Calculate the following binomial probability by either using one of the binomial probability tables, software, or a calculator using the formula below. Round your answer to 3 decimal places. P(x | n, p) = n! (n − x)! x! · px · qn − x where q = 1 − p P(x = 14, n = 16, p = 0.80) =
Calculate the following binomial probability by either using one of the binomial probability tables, software, or a calculator using the formula below. Round your answer to 3 decimal places. P(x | n, p) = n! (n − x)! x! · px · qn − x where q = 1 − p P(x = 11, n = 13, p = 0.80) =
Calculate the following binomial probability by either using one of the binomial probability tables, software, or a calculator using the formula below. Round your answer to 3 decimal places. P(x | n, p) = n! (n − x)! x! · px · qn − x where q = 1 − p P(x > 10, n = 15, p = 0.8) =
Calculate the following binomial probability by either using one of the binomial probability tables, software, or a calculator using the formula below. Round your answer to 3 decimal places. P(x | n, p ) = n! (n − x)! x! · px · qn − x where q = 1 − p P(x < 4, n = 10, p = 0.4) = If you can please explain to me how to do this besides just the answer?
4. (20 pts.) [Bonus Question) Suppose that X is a Binomial RV with p=0.5 i.e. X ~ Bin(n,0.5). Find the probability mass function of the transformation Y = 2X.