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- If X1, X2, and X3 constitute a random sample of sizen = 3 from a Bernoulli population, show that Y =X1 + 2X2 + X3 is not a sufficient estimator of θ. (Hint:Consider special values of X1, X2, and X3.)Suppose x has a distribution with μ = 21 and σ = 11. (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 = 21 and σ x = 11.Yes, the x distribution is normal with mean μ x = 21 and σ x = 2.75. No, the sample size is too small.Yes, the x distribution is normal with mean μ x = 21 and σ x = 0.7. (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 = 21 and σ x = 2.75.Yes, the x distribution is normal with mean μ x = 21 and σ x = 0.7. Yes, the x distribution is normal with mean μ x = 21 and σ x = 11.No, the sample size is too small. Find P(17 ≤ x ≤ 22). (Round your answer to four decimal places.)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.)
- Suppose x has a distribution with μ = 78 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 = 78 and σ x = 2. Yes, the x distribution is normal with mean μ x = 78 and σ x = 0.5. Yes, the x distribution is normal with mean μ x = 78 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 = 78 and σ x = 2. Yes, the x distribution is normal with mean μ x = 78 and σ x = 0.5. Yes, the x distribution is normal with mean μ x = 78 and σ x = 8. No, the sample size is too small. Find P(74 ≤ x ≤ 79). (Round your answer to four decimal places.)Suppose x has a distribution with μ = 62 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 = 62 and σ x = 2.Yes, the x distribution is normal with mean μ x = 62 and σ x = 0.5. Yes, the x distribution is normal with mean μ x = 62 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 = 62 and σ x = 2. Yes, the x distribution is normal with mean μ x = 62 and σ x = 0.5. Yes, the x distribution is normal with mean μ x = 62 and σ x = 8. No, the sample size is too small. Find P(58 ≤ x ≤ 63). (Round your answer to four decimal places.) Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 87 tons…If X1, X2, ... , Xn constitute a random sample from anormal population with μ = 0, show that ni=1X2inis an unbiased estimator of σ2.
- 1 The discrete random variable X has Var (X) = 5 Find Var (4X – 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. ________…