Question

please be as clear as possible, take note of units and significant figures. thanks for the help

PART 1. For each of the following statements, circle the letter “T” if it is true, and “F” if it is false. TF If events A and B are mutually exclusive, they must be independent. т F P[A B C] P[CB] P[B] = P[CAB] P[AB] P[B]. T F If the 95% confidence interval for a particular situation is (-5,5), then the 90% confidence interval would be narrower; that is, (-5 + x, 5 - x), where x > 0. TF For a continuous random variable X, if its PDF f(x) is constant, then X is uniformly distributed TF The CLT (Central Limit Theorem) states that the distribution of the sample mean X approaches the normal distribution with mean u and variance o2 if the Xi's (i = 1, 2, ..., M) are identically distributed with mean u and variance oʻ, as N becomes sufficiently large. T F Let û x, and Û2 x, be two estimators for the population mean. û, is a better estimator than ûj. PART 2. From the list below, place on the left of the formula the number of the correct label next to each symbol. Some labels may be used more than once, some others may not be used. 1. Population mean 2. Population variance 3. Population standard deviation 4. Sample mean 5. Sample variance 6. Sample standard deviation 7. 8. 9. 10. 11. 12. Variance of sample mean Standard deviation of sample mean Sample variance of sample mean Sample standard deviation of sample mean Error mean square None of the above E[X] (N-1)N E[(x - 21 N E[X4) -u? OX S #$&; – F) X E[( X - u)?] N

Answer 1

3 solution : PART-1 O False (F) It is because it A and B ane mutually exclusive then pland) = 0 It A and B are independent then PlanB) =P(AP(B) de mutually exclusive event not be independent 2 we have below foumula 1031 three events probability 8031 three events Conditional PCANBNC) - P(Albnc) P(CIB) PCB) > 0 PIANBNC) = P(Cland) P(A/B) PCB) is from and ☺ Palenc) PCC1B) PCB) - PCC1ANB) P(A/B) PCB) :: It is Thue (T). Rule:-) confidence level increase then confidence interval length also increase and vice-varse. os ab 95% confidence interval for a particular situation is 6-5,5) then the 90% confidence interval would be nachower, that is is true 1-5+2, 5-X), where 270 és Answer ;→ True (1) * True (1) :given statement that continuous random Vevlable x, it its, PDF fa) is constant, theo x is uniformly Pouue (T) :> given statement of centeral limit theorem © False (F) :-> Bt sample size is greater then better estimator Value tou population → In û sample size is 9 and in ű, sample size is 8. és û, is better estimatou than ù. PART :-2 Population mean = Il 1 population variance ☺ population Standard deviation - Ox E[(x-2)] N. Sample mean = X = E(X) Sample Valante (x-3) 14 distributed. 5 8 tấe . ECC X-4?] N. s13 A 5

6 Sample Standard deviation = None of the above * variance of sample mecin = E (?)-42 Standard deviation of sample mean= None of the above Sample variance of Sample mean = să Sample standard deviation of sample mean = None of the above. mean square (X; -ā). 19 10 -12 Error

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