2 [Short Answer】 (1) Suppose that X random variable with E(X)=10,Var (X) = 2, Estimate P7< X<13}≥_
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[Short Answer]
(1) Suppose that X random variable with E(X)=10,Var (X) = 2,
Estimate P7< X<13}≥_
(2) Suppose that X random variable for which E(X)=10,P(X ≤7)=0.2.
and P(X213)=0.3.Prove that Var(X) 29/2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96b78458-8787-40e8-a189-ed7c6f48638f%2F8bc56c40-1e23-41f8-869b-07d34159c3f6%2Fy6nanh_processed.png&w=3840&q=75)
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- Suppose that the test score of a student taking the final of a probability course is a random variable with mean 80. (a) Give an upper bound for the probability that a student's test score will exceed 90. P{score > 90} < (b) Suppose that we know, in addition, that the variance of students' test scores on the final is 30. What can you say about the probability that a student will score between 70 and 90 (do not use the central limit theorem)? P{70 < score < 90} ? (c) How many students would have to take the final to ensure with a probability of at least 0.95 that the class average would be within 3 of 80 (do not use the central limit theorem)? n = (d) If you use the central limit theorem in (c), what is your estimate for the number of students needed? п —1 (a) Discuss the two expressions -x;- )² and E(x;- )², both of which are used (n-1) i=1 to measure the spread of a set of observations x1, x2, . .., X. (b) A random sample of n observations is taken from a distribution; the sum of the observations is t, and the sum of the squares of the observations is 12. Explain how to estimate the mean and the variance of the distribution from which the random sample was taken. (c) Given the random sample described in part (b), write down expressions (based on 11 and t2) for estimates of the mean and variance of the mean of a further, independent, random sample of size m , from the original distribution. (d) Given that n = 25, 1, = 400 and t2 = 8800, construct a 99% confidence interval for the mean of the distribution, and use it to test whether or not this mean could be 20.The standard error of the mean is the standard deviation of the sampling distribution of the sample means (1) The standard deviation of the sampling distribution of the mean is always smaller than the standard deviation of the population under study unless n-1 and then they're equal () For a sampling distribution of the means, 90% of the means would be between 1.96 standard deviations Multiple Choice O (0) and are correct statements but not to (1) and (0) are correct statements but not ( 0,00 and are all correct statements (and (i) are correct statements but it
- please only do: if you can teach explain eachIf P(B) = ² and P(A'^B) = 12, for two events A and B, find P(A/B).What is the variance and standard deviation for the number of times the SAT is taken? x Frequency (f) fx f*x2= (f*x) x (x) (4) = (3)x(1) 5152727-(2547473)(2547473)/1518859=880035.3688/1518859=0.5794 (1) (2) (3)=(1)x(2) (4)=(3x1) Population Variance 1 721,769 721,769 721,769 2 601,325 1,202,650 2,405,300 3 166,736 500,208 1,500,624 4 22,299 89,196 356,784 5 6,730 33,650 168,250 Total 1,518,859 2,547,473 5,152,727 880035.3688 0.5794 n=1,518,859 ∑fx = 2,547,473 The population variance is 0.5794 The Standard Deviation? 0.76 Can you show me the steps to reach the standard deviation of .76 ?
- Consider again the random variable with a cumulative distribution function ofF(x) = x^2/25, for 0 ≤ x ≤ 5. (d) What is the probability of x =1? (e) Do you think x is a symmetric random variable? Why or why not? I need answers of sub-parts (d) and (e) only.let Y be a single observation from a normal distribution with mean θ and variance θ^2, θ>0.derive maximum likelihood estimator(s) of the underlying parameter(s) *In detailed
- For each random variable defined, describe the set of possible values for the variable, and state whether the variable is discrete or continuous. (a) U = number of times a surfer has to paddle in front of a wave before catching one (b) X = length of a randomly selected angelfishSuppose X1, ..., Xn have been randomly sampled from a normal distribution with mean 0 and unknown variance sigma^2, and let U = c * i=1 -> n summation (X_ i)^2 , where c is a constant. Find the value of c that minimises the Mean Squared Error (MSE)An automobile manufacturer has developed a new type of bumper, which is supposed to absorb impacts with less damage than previous bumpers. The manufacturer has used this bumper in a sequence of 25 controlled crashes against a wall, each at 10 mph, using one of its compact car models. Let X = the number of crashes that result in no visible damage to the automobile. 1.The (parameter/random_variable/statistics/variable) , [variable],[statistics],[random_variable] to be estimated is p. 2. Continuing this question, p the is (percentage/median/average/poportion) of such crushes that result in no damage [alternatively, p = P(no damage in a single crash)]. Select the correct answer from the options inside the (bracket).
