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- 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.Suppose you know that Var(Z)=(k+1)E(Z) where k is 7. Determine the distribution of Z and find its parameter(s), explaining your argument carefully.3. If X has an exponential distribution with λ=2. Calculate the following The value of x such that P(X<x)=0.05 corresponds to x=?
- Use R and your calculator to calculate the following.(a) P(X > 7), X has an F-distribution with 5 numerator df and 10 denominator df.(b) P(X > 7), X has an F-distribution with 15 numerator df and 10 denominator df.(c) P(3 < X < 15), X has an F-distribution with 5 numerator df and 10 denominator df.1.Given t distribution, find values of t(5)0.2 2.explain the relations between them with Z0.2If X1, X2, ... , Xk have the multinomial distribution of Definition 8, show that the mean of the marginal distribu-tion of Xi is nθi for i = 1, 2, ... , k.
- T has an exponential distribution such that P(T≤2)=2P(T>4) What is Var(T)=?Not sure how to answer questions C through E. Suppose that X has a (continuous) uniform distribution between 10 and 20 (a) Compute E (X). (b) Compute Var (X). (c) Compute P (X < 12). (d) Compute P (X > 12). (e) Compute P (X < 8 or X > 22).Let X ~ U[0,1] and Y = -βln(1-X). What is the distribution of Y? Justify.
- Suppose the reaction temperature X (in °C) in a certain chemical process has a uniform distribution with A = −6 and B = 6. (a) Compute P(X < 0) (b) Compute P(−3 < X < 3). (c) Compute P(−4≤ X ≤ 5). (Round your answer to two decimal places.)A random sample of n = 12 individuals is selected from a population with µ = 70, and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M = 74.5 with SS = 297. Use the Distributions tool to help answer the questions that follow. t Distribution Degrees of Freedom = 21 -3.0-2.0-1.00.01.02.03.0x.5000.50000.000 How much difference is there between the mean for the treated sample and the mean for the original population? (Note: In a hypothesis test, this value forms the numerator of the t statistic.) If there is no treatment effect, how much difference is expected just by chance between the sample mean and its population mean? That is, find the standard error for M. (Note: In a hypothesis test, this value is the denominator of the t statistic.) Based on the sample data, does the treatment have a significant effect? Use a two-tailed test with α = .05. (Show three…In this question you are required to examine distribution at X(0) and x(1/8fo) x(0) ∈{0,-1 ,1} X(1/8fo)∈{1/(√2), -1/(√2)} Show that is not strict sense stationary
