(d)In an experiment, n fair coins are tossed. The probability of getting head is p and eachtoss is independent. Each coin that shows tails is tossed again. Let Xbe the total numberof heads.(i)Verify that X is a binomial distribution. Specify its parameter(s).(ii)What is the probability mass function of the total number of heads X ?

A discrete probability distribution counts occurrences that have countable or finite outcomes.…

Answered: (d) In an experiment, n fair coins are…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Because all airline passengers do not show up for their reserved sear an airline sells n=125 tickets for a flight that holds only 120 passengers. The probability that a passenger does not show up is 0.10 assume that the passengers behave independently.
A Bus driver proposed a snow day with the distribution below, where x is defined to be the number of days that classes are canceled per week for a week where multiple storms are for cast. He proposes the probability mass function P(x) = 5/5 for x = 1,2,3,4,5 a) Show that the pmf is well defined b) Determine Mx, also called the expected value of x. Interpret the result and explain if the value for Mx makes sense.
The experiment is to toss two balls into four boxes in such a way that each ball is equally likely to fall in any box. Let X denote the number of balls in the first box. Find the probability mass function and distribution function of X.
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Dppp5
Use the probability distribution to complete parts (a) and (b) below. The number of defects per 1000 machine parts inspected 3 Defects 1 4. Probability 0.262 0.299 0.233 0.153 0.037 0.016 ... (a) Find the mean, variance, and standard deviation of the probability distribution. The mean is (Round to one decimal place as needed.)
A motorcycle drives from Welcome Rotonda to Fairview and back using the same course everyday. There are four stoplights on the course.Let x denote the number of red lights the motorcycle encounters going from Welcome Rotonda to Fairview and y denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (x, y) is given by 2 3 0.07 0.01 0.05 0.01 0.03 0.01 0.03 0.08 0.03 0.02 2 0.03 0.11 0.15 0.01 0.01 3 0.02 0.07 0.1 0.03 0.01 4 0.01 0.06 0.03 0.01 0.01 Find: 1. Standard deviation of Y. 2. Fill in the blanks As the number of motorcycle drivers from Welcome Rotonda to Fairview encountered by the motorcycle (increase, decrease, or be (zero, negative, or positive) covariance. The increases, the number of stoplights of its return trip tends to uncorrelated). Therefore, X and Y have a covariance was calculated to be (numerical value). *Describe the correlation whether a strong, a weak, or no. X and Y have correlation.…
A fair coin is tossed repeatedly until head appears for the third time. Calculate the mean and variance of the total number of tails that show up. Let X be the random variable that denotes the total number of tails that show up. Write down the probability mass function and cumulative distribution function of X.
A company has seven applicants for two positions: three women and four men. Suppose that the seven applicants are equally qualified and that no preference is given for choosing either gender. Let x equal the number of women chosen to fill the two positions. (a) Write the formula for p(x), the probability distribution of x. (b) What are the mean ? and variance ?2 of this distribution? (Round your mean to one decimal place and your variance to two decimal places.)
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Suppose we roll 3 fair dice and let X be the number of twos we roll.(a) Find the probability mass function of X.(b) Find the expected value of X.(c) Find the variance of X.(d) Find the probability-generating function of X.(e) Find the moment-generating function of X
Exercise(3): If the mean and variance of a binomial distribution are 9 and 6 respectively, then find: (1) The probability mass function P(x = k) (2) P(x=3) (3) P(x>1)

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