Given that the moment generating function of a random variable X is e"12, using the Maclaurin series, obtain the moments for this random variable. Demonstrate your work clearly. Study the pattern and report the general form, if possible.
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- Assume that a procedure yields a binomial distribution with a trial repeated n=5n=5 times. Use some form of technology to find the probability distribution given the probability p=0.6p=0.6 of success on a single trial.(Report answers accurate to 2 decimal places.) k P(X = k) 0 1 2 3 4 5In each part, assume the random variable X has a binomial distribution with the given parameters. Compute the probability of the event. (a) n = 6, p = 0.7 Pr(X = 5) = (b) n = 4, p = 0.5 Pr(X = 0) = (c) n = 6, p = 0.8 Pr(X = 1) = (d) n = 3, p = 0.1 Pr(X = 1) =The following table gives the total endothermic reactions involving sodium bicarbonate Final Temperature Conditions Number of Reactions 266 K 271 K 60 274 K 92 Assume that reactions are independent. What is the probability that the 2nd reaction to result in a final temperature less than 272K occurs within three or fewer reactions? Report answer 3 decimal places.
- 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 XAssume that a procedure yields a binomial distribution with a trial repeated n=5n=5 times. Use some form of technology to find the probability distribution given the probability p=0.224p=0.224 of success on a single trial.(Report answers accurate to 4 decimal places.) k P(X = k) 0 1 2 3 4 5Preferred if solved via R. Currently need help understanding R concepts.
- records over the past year show that 1 out of 395 loans made by mammon bank have defaulted. find the probability that 5 or more out of 280 loans will default. hint: is it appropriate to use the poisson approximation to the binomial distribution? (round λ to 1 decimal place. use 4 decimal places for your answer.) I do not wish for the answer to this one but if i could get an example with differnt numbers with the answer. Thank you.Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(X) using the normal distribution and compare the result with the exact probability. n=56 p=0.5 x=30 A)For n=56, p=0.5, and X=30, use the binomial probability formula to find P(X). B)Can the normal distribution be used to approximate this probability? A. No, because np(1−p)≤10 B. Yes, because np(1−p)≥10 C. Yes, because np(1−p)≥10 D. No, because np(1−p)≤10 C) Approximate P(X) using the normal distribution. Use a standard normal distribution table. A. P(X)=enter your response here (Round to four decimal places as needed.) B. The normal distribution cannot be used. D) By how much do the exact and approximated probabilities differ? A.enter your response here (Round to four decimal places as needed.) B. The normal distribution cannot be used. E)By…ON QUESTION F HOW WOULD I SHOW THE EVENT IN EXCEL FORMULA?
- Telephone calls arrive at an exchange according to the Poisson process at a rate A= 2/min. Calculate the probability that exactly two calls will be received during each of the first 5 minutes of the hour.Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(X) using the normal distribution and compare the result with the exact probability. n=51 p=.03 x=20
