Suppose X1, .,Xn is a random sample from a N (H, o²) opulation, and independently, Y, ....,Ym is a random sample om N(n, y²) population. Find minimum sufficient statistics for e following three cases
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Q: At the Blood Bank, they know that O+ blood is the most common blood type and that 40% of the people…
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- Suppose that the random variables X1,...,Xn form a random sample of size n from the uniform distribution on the interval [0, 1]. Let Y1 = min{X1,. . .,Xn}, and let Yn = max{X1,...,Xn}. Find E(Y1) and E(Yn).Let X1, X2, ... , Xn be a random sample, normally distributed with mean μ and variance σ2If σ2 is known, find a minimum value for n to guarantee that a 0.95 CI for μ will have length no more than σ/4Let X1, X2, ... , Xn be a random sample, normally distributed with mean μ and variance σ2If σ2 is unknown, find a minimum value for n to guarantee, with probability 0.90, that a 0.95 CI for μ will have length no more than σ/4 explain.
- 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.Let X1, X2, ... , Xn be a random sample, normally distributed with mean μ and variance σ2If σ2 is unknown, find a minimum value for n to guarantee, with probability 0.90, that a 0.95 CI for μ will have length no more than σ/4Suppose that three random variables X1, X2, X3 form a random sample from the uniform distribution on interval [0, 1]. Determine the value of E[(X1-2X2+X3)2]
- Suppose that the continuous two-dimensional random variable (X, Y ) is uniformly distributed over the square whose vertices are (1, 0), (0, 1), (−1, 0), and (0, −1). Find the Correlation Coefficient ρxyAt the Blood Bank, they know that O+ blood is the most common blood type and that 40% of the people are known to have O+ blood. Blood type A- is a very scarce blood type and only 6% of the people have A- blood. Half of the people have blood type A or B. Let: X= number of people who have blood type O+ Y= number of people who have blood type A- Z= number of people who have blood type A or B Consider a random sample of n=9 people who donated blood over the past three months. a) The expected number of people with blood type O+ is _____and the expected number of people with blood type A- is ______Round your answers to 2 decimal places. b) Calculate the following probabilities: P(X=5)=_________ Round your answer to 4 decimal places. P(X>2)=_________ Round your answer to 4 decimal places.Suppose the random variable y is a function of several independent random variables, say x1,x2,...,xn. On first order approximation, which of the following is TRUE in general?
- A congressional committee is composed of 10 members: 6 Republicans and 4 Democrats. On any given vote, members vote independently. Whereas Republicans always vote their party line, Democrats vote their party line with probability .8, and vote Republican with probability .2. On a rainy day only 3 committee members (selected w/o replacement) were present. Let X = number of Democrats present Y = Number who voted Democratic that day Find the marginal pdf of X, i.e., P[X=k] for k=0, 1, 2, 3. Display E[X] and VAR[X]. Determine the conditional probability that P[ Y=j | X=k] for k=3 and j=0,1,2,3 Display the table of joint probabilities fX,Y(i,j) for 0 ≤ j ≤ i, i=0,1,2,3 Display the marginal pdf of Y. Is it recognizable? Compute E[Y]and VAR[Y]. Determine the conditional expectation of Y given that X=x, for x=0,1,2,3.…At the Blood Bank, they know that O+ blood is the most common blood type and that 40% of the people are known to have O+ blood. Blood type A- is a very scarce blood type and only 6% of the people have A- blood. Half of the people have blood type A or B. Let: X= number of people who have blood type O+ Y= number of people who have blood type A- Z= number of people who have blood type A or B a) Consider a random sample of n=9 people who donated blood over the past three months. The expected number of people with blood type O+ is and the expected number of people with blood type A- is Calculate the following probabilities: P(X=5)= __________ Round your answer to 4 decimal places. P(X>2)= __________ Round your answer to 4 decimal places. b) Consider a random sample of n=40 people who donated blood over the past three months. Use the relevant probability function of Y to calculate the probability that 2 people in the random sample will have type A- blood. ________…Suppose x has a distribution with μ = 84 and σ = 8. (a) If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means? Yes, the x distribution is normal with mean μ x = 84 and σ x = 2.Yes, the x distribution is normal with mean μ x = 84 and σ x = 0.5. Yes, the x distribution is normal with mean μ x = 84 and σ x = 8.No, the sample size is too small. (b) If the original x distribution is normal, can we say anything about the x distribution of random samples of size 16? Yes, the x distribution is normal with mean μ x = 84 and σ x = 2.Yes, the x distribution is normal with mean μ x = 84 and σ x = 0.5. Yes, the x distribution is normal with mean μ x = 84 and σ x = 8.No, the sample size is too small. Find P(80 ≤ x ≤ 85). (Round your answer to four decimal places.)