SOLVE STEP BY STEP IN DIGITAL FORMAT 1. Show that the function F given by F(x) = { 1 is distribution and calculates 0 - x < 3 x ≥ 3 • P(X EN) • P(5 < X < 7) • P(X > E(X))
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- Suppose that the lifetime in years, X, of a type of electrical switch follows the distribution f(x)=12e−x2f(x)=12e−x2for x>0x>0. What type of continuous distribution is this and what is the average lifetime of one of these switches?Suppose that you enter a fantasy baseball league. Suppose that the 2021 team budget, say , is randomly drawn from a uniform distribution on the interval , where the unit is U.S. million dollars. In addition, suppose that after the value has been observed , the 2022 team budget, say , is randomly drawn from a uniform distribution on the interval . In other words, the 2022 budget is at most as large as the 2021 budget. a) For any given value of x(50<x<350), obtain E[Y|X=x] b) In view of part (a), obtain E[Y|X] c) Atlanta Braves won the 2021 World Series title. Their estimated 2022 payroll is about $130 million. Would your 2022 fantasy baseball budget be on average larger than their 2022 payroll? Explain briefly.If Y has a binomial distribution with n trials and a probability of success p, show that the functiongenerator of moments for Y is: m(t) = (pe' +q)n with q = 1− p
- Solve c and d showing all workings and using the t distribution tablesuppose x has an exponential distribution with B=1/8 , then P(X>1)For the given Problem, suppose that the probability of concluding that the process is out of control when it is actually in control is set at .02. Find the upper and the lower control limits for the resulting X- chart.
- The U.S. divorce rate has been reported as 3.6 divorces per 1000 population. Assuming that this rate applies to a small community of just 500 people and is Poisson distributed, and that x = the number of divorces in this community during the coming year, determine the following: a. E(x) P(x=1) c. P(x= 4) d. P(x6) e. P(2x5)Suppose that x has an exponential distribution with θ =1.5. Find P(x > 1The U.S. divorce rate has been reported as 3.6 divorces per 1000 population. Assuming that this rate applies to a small community of just 500 people and is Poisson distributed, and that x = the number of divorces in this community during the coming year, determine the following: a. E(x) b. P(x=1) c. P(x= 4) d. P(x6) e. P(2x5)
- If Xhas the Poisson distribution with P(X=1) = 2P(X=2), then P(X ≥ 2) is approximately:What is the Discrete Variable Variance for the following numbers:x = 0 and P(X = x) = 0.71x = 1 and P(X = x) = 0.17x = 2 and P(X = x) = 0.01x = 3 and P(X = x) = 0.11Find P(X=4) if X has a Poisson distribution such that 3P(X=1)=P(X=2)
