Consider a multinomial distribution with three possible outcomes. The distribution of X1 isbinomial with parameters K, K-k¡ and k. Give both analytical and probabilistic proofs.

A multinomial distribution is considered with possible outcomes.It must be shown analytically and…

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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In a digital communication channel, assume that the number of bits received in error can be modeled by a binomial random variable, and assume that the probability that a bit is received in error is 0.0001. If 150,000 bits are transmitted, what is the probability that errors are between 10 and 18? How to compute P(X=10)= (150000c10)(0.0001)10(1-0.0001)150000-10
Suppose 22% of students at a certain university are out of state students. A professor takes a random sample of 50 students. Let X = the number of out of state students in the sample. Determine if X is binomial by stating and checking all four requirements. If X is binomial, summarize the distribution of X in shorthand notation.
Consider a multinomial distribution with three possible outcomes. The distribution of X¡ is binomial with parameters K, K-k¡ and k. Give both analytical and probabilistic proofs.
You find 6 statements below. Each statement is either true (T) or false (F) (write yourchoice in the table). 1) In a probability model, all possible outcomes together must have a probabilityof 1.2) A density curve describes the probability distribution of a discrete randomvariable.3) Outliers do not have a large effect when we calculate the mean.4) The probability of success for binomial distribution must remain the same foreach trail.5) In the Normal distribution with mean μ and standard deviation σ, approximately95% observations fall within ± 2σ of the mean μ.6) Since the median is the middle value of a data set it must always be smaller thanthe mean.
A multiple choice calculus test has 5 questions. Each question has five possible choices with only one choice being the correct answer. Let X be the number of questions the student gets correct. (a) List the conditions of the binomial setting, does X follow a binomial distribution? If so, identify n and p. If not, explain why not. (b) What is the probability that a randomly selected student writing the test will get at least 40% on the test?
A professional basketball player has an 81% success rate when shooting free throws. Let the random variable X represent the number of free throws he makes in a random sample of 10 free throws (assume this experiment meets all binomial requirements). What is the probability that he makes exactly 7 of the 10 free throws? Note: You do not need to solve for the exact probability; you just need to choose the equation below that correctly represents how you would solve for this probability. 10! -(0.81)7(0.19)10 3!7! P(X=7) a. 10! P(X=7) = (0.81)7(0.19)³ O b. 7! 10! P(X=7) = (0.81)7(0.19)3 C. 3! P(X=7) = d. 10! -(0.81)3(0.19)7 3!7! 7! P(X=7) = 3! -(0.81) (0.19)7 е. P(X=7) = Of. 10! -(0.81)7(0.19)3 7!3!
Bart Simpson takes a multiple choice exam in his Statistics 101 class. The exam has 16 questions, each has 4 possible answers, only one of which is correct. Bart did not study for the exam, so he guesses independently on every question. Let X denote the number of questions that Bart gets right. Round all answers to 4 decimal places. 1. Verify that it is appropriate to use the Binomial model to calculate probabilities for Bart's success on the exam by confirming the 4 criteria. State each criteria and why each is met. Include symbols and values for the number of trials and the probability of success.
Give the analytical and probabilistic proofs. Consider a multinomial distribution with three possible outcomes. The distribution of X1 is binomial with parameters N, N-n1 and n.
Of 9 randomly selected male students, Xj used Apple computer, whereas of 12 randomly selected female student, X2 used Apple computer. Let: p1 and p2 denote the probabilities that a randomly selected male and female students, respectively, played tennis. what is unbiased estimator of P1 - P2 ? X2 Da. 7+ 12 X1 X2 Ob. 49 144 X2 12 X1 Od. 49 X2 144
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Consider a multinomial distribution with three possible outcomes. The distribution of X₁ is binomial with parameters K, K-k₁ and k. Give both analytical and probabilistic proofs.