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prove the theorem
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- A research center claims that 26% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 700 adults in that country, 28% say that they would travel into space on a commercial flight if they could afford it. At α=0.10, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below.If a dealer’s profit, in units of $5000, on a newautomobile can be locked upon as a random variable X having thedensity function f(x) = 2x(1-x), 0<x<1, Find the average profit per automobile.Suppose that X1, . . . , Xn form a random sample from the uniform distribution on the interval [θ1, θ2], where both θ1 and θ2 are unknown (−∞ < θ1 < θ2 < ∞). Find the MOM estimates of θ1 and θ2.
- A marketing research group found that 25% of the 200 shoppers, it recently interviewed at a certain shopping center, resided more than 12 miles from the center. Assume that a random sample was taken, construct a 95% C.I. for the actual; percentage of shoppers who live more than 15 miles from that center.A die is loaded in such a way that the probability of the face with j dots turning up is proportional to j^2 for j = 1, 2, 3, 4, 5, 6. What is the probability of rolling at most three sixes in 5 independent casts of this die?A research center claims that 30% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 1200 adults in that country, 33% say that they would travel into space on a commercial flight if they could afford it. At α=0.05, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below. Identify the P-value?
- Let � be a random variabale satisfying �(0,1).Without using the normalcdf(...) function, find �(�≤-2).Assume that the coin is weighted so that Pr[H]=59, and that the coin is flipped until a head appears, or 3 consecutive tails appear. The random variable X is defined to be the total number of flips of the coin. How many different values are possible for the random variable X?
