Let the three mutually independent events C₁, C₂, and C3 be such that P(C₁) = P(C₂) = P(C3) = 1/4. Find P((C₂NC₂UC₂).
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- m 8. Show that Σ (7) (p²k) = (m+p). k=0TF.12 The joint pdf of the lifetimes X and Y in years of two batteries working in parallel is (see picture) a) Find the probability P(Y ≤ 0.5). b) Find the expected values E(X) and E(XY).K:56) Somehow you manage to build a fair 3-sided die, equally likely to show 1, 2, or 3 every time it is rolled. You roll the die twice, with the results each time being independent. If X is the maximum of the 2 numbers rolled and Y is the sum of the 2 numbers rolled, find the correlation ρ(X, Y ).
- An individual has a vNM utility function over money of u(x) = Vx, where x is final wealth. Assume the individual currently has $16. He is offered a lottery with three possible outcomes; he could gain an extra $9, lose $7, or not lose or gain anything. There is a 15% probability that he will win the extra $9. What probability, p, of losing $7 would make the individual indifferent between to play and to not play the lottery? (Make sure to answer in the form, 0.X, i.e. 0.25) Enter your answer hereGiven a pdf that is N(7, 5 2) find P(|x-5|>3A research center claims that 31% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 800 adults in that country, 34% say that they would travel into space on a commercial flight if they could afford it. At a = 0.10, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below. (a) Identify the claim and state H, and H Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) O A. At least % of adults in the country would travel into space on a commercial flight if they could afford it. O B. % of adults in the country would travel into space on a commercial flight if they could afford it. %. O C. The percentage adults in the country who would travel into space on a commercial flight if they could afford it is not O D. No more than % of adults in the country would…
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- Let X; be random variables and M; (t) be their respective moment generating functions, for i = 1, 2, 3. Solve: Suppose that M₁ (t) = 1 +t+t² + t³+... Is this enough information to determine the type of random variable that X₁ is? Explain why or why not. Determine the type of random variable if there is enough information. Determine if it is possible for M₂ (t) = (-1)" -0 (2n)! possible, determine the type of random variable that X₂. -+2n. Explain why or why not. If it is Suppose that that the expectation of X3 is -1 and its second moment is 1. Determine if this is enough information to find the moment generating function of X3 explicitly. Explain why or why not. If it is enough information, compute it explicitly.A medical researcher says that less than 85% of adults in a certain country think that healthy children should be required to be vaccinated. In a random sample of 300 adults in that country, 83% think that healthy children should be required to be vaccinated. At α=0.01, is there enough evidence to support the researcher's claim? Complete parts (a) through (e) below. (a) Identify the claim and state H0 and Ha. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. Less than enter your response here% of adults in the country think that healthy children should be required to be vaccinated. B. The percentage of adults in the country who think that healthy children should be required to be vaccinated is not enter your response here%. C. More than enter your response here% of adults in the country think that healthy children…A student goes to the library. Let events B=B= the student checks out a book and D=D= the student check out a DVD. Suppose that P(B)=0.59PB=0.59, P(D)=0.45PD=0.45 and P(D|B)=0.50PD|B=0.50. Round each answer to four decimal places. Find P(B′) Find P ( D and B) Find P (B\D) Find P (D and B') Find P (D\B')
