5 Show that mean of the binomial distribution is the product of the parameter p and. the nurmhar of tirag
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- The moment generating function of the negative binomial distribution is given by m,)-ge pe' . Derive the mean of the distribution using the mgf. 1- qe'Suppose that the lifetime of a component (in hours) is modeled with a Weibull distribution 4000. Determine the following in parts (a) and (b): with B 2 and 8 = = a P(X > 5000) b P(X> 8000|X > 3000) c Comment on the probabilities in the previous parts compared to the results for an expo- nential distribution.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.
- Let X be the number of scoring chances that result in goals for a football team during n scoring chances. During many games, the team scores on 20% of the chances. a) Explain why it might be reasonable (at least as an approximation) to assume that X is binomially distributed in this situation. Do this by going through each of the points that must be met for us to use the binomial distribution, assess whether it is reasonable for them to be met here and specify any additional assumptions we need to make.Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)Let x be a random variable that represents the weight of a lion in a certain region of Africa. Assume that x is normally distributed with a mean = 260 lbs . With standard deviation =30 lb Please include the graphs for questions A and B
- According to recent data, 45% of the U. S. adults have hypertension. A random sample of 750 adults in the U.S. is selected. Let X represent the number that have hypertension. a. Under what condition will this binomial distribution be bell-shaped? State this condition and verify that that condition is met here. Show the calculation required.Write the sufficient statistics for the parameter of binomial.Suppose that the contagious period of COVID-20 has an average of 7 days, and follows a chi-square distribution. Let X measure the contagious period for a randomly selected specimen of the COVID-20 virus. State the distribution of the random variable X. Group of answer choices X∼χ2(6) X∼Student′st(7) X∼χ2(7) X∼Continuous(7) A friend of yours has COVID-20 and the doctors have told her that she has had it for 10 days. Compute the probability that they are still contagious. (I.E. compute the probability that X is greater than or equal to 10 days.)
- 1 find the first four moments of the binomial distribution 9. Ifx is a binomial variate with parameters 6 and 2 about origin.The profits of a mobile company are normally distributed with Mean of R.O (17x 10) and standarddeviation of R.O (17).a. Find the probability that a randomly selected mobile has a profit greater than R.O ((17x10) +10)2. Use the normal approximation to the binomial with n=10 and p=0.5 to find the probability P(X27)
