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3. Let Y.Y,...,Y be independent random variables with Binomial distribution with parameters: (number of trails) ni, 12,...,nk respectively, and the same p (probability of success in trials). Derive the probability distribution of U = Y1 + Y2 + ... +Yk.

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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

What are the four conditions necessary for x to have a binomial distribution? Mark all that apply.

A) The probability of success, p, is constant from trial to trial.

B) There can only be two outcomes, success and failure.

C) The trials must be independent.

D) You must have at least 10 successes and 10 failures.

E) X can take on any value in an interval.

F) X counts the number of trials until you get a success.

G) There are n set trials.

MUST BE COMPLETED IN MINITAB

Module 3 Minitab Assignment

Instructions:

Below you will find questions. Please use the provided data to complete the tasks and to answer the questions.

Produce the probability histogram (probability distribution plot) of each of the following and state if the distribution is symmetric, skewed to the left, or skewed to the right.

The binomial distribution with n = 20 and p = 0.2.

The binomial distribution with n = 30 and p = 0.48

The binomial distribution with n = 15 and p = 0.8.

Suppose X is a binomial random variable with n = 35 and p = 0.67.

What is the probability that X is exactly 20?

What is the probability that X is at most 27?

What is the probability that X is at least 15?

Consider 3 trials, each having the same probability of success. Let X denote the total number of successes in these trials. If E[X]=1.8, what is (a) the largest possible value of P{X=3}? (b) the smallest possible value of P{X=3}? In both cases, construct a probability scenario that results in P{X=3} having the stated value. Hint: For part (b), you might start by letting U be a uniform random variable on (0, 1) and then defining the trials in terms of the value of U.

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