Suppose F and H are events in the same sample space for some experiment. If we know Pr[F]=, Pr[H] = 1, and Pr[Fn H] = ½, determine Pr[H | F], 27
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![Suppose F and IH are events in the same sample space for some experiment. If we know Pr[F] = 4. Pr[H] = 4, and Pr[Fn H] = 3, determine Pr[H | F].
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- Let X denote the sample average for a random sample with mean uu and variance 02. Consider the following estimator for u: W=n+2/n+1°X Is W as consistent estimator of u? a. Yes b. No c. It dependsYou receive a brochure from a large university. The brochure indicates that the mean class size for full-time faculty is fewer than 32 students. You want to test this claim. You randomly select 18 classes taught by full-time faculty and determine the class size of each. The results are shown below. At α = 0.01, can you support the university’s claim?35 28 29 33 32 40 26 25 29 28 30 36 33 29 27 30 28 25Suppose that the response time X of a subject to a stimulus is N(15, 16). If n-16, then the probability of the sample mean greater than 12 is: a. 0.9772 Ob. 0.9987 Oc. 0.0013 Od. 0.7899
- 17. Conditional Distributions Consider two random variables X and Y for which we know Pr(X = x) = Pr(X = x|Y = y)for all possible values of x and y. In this case we would say that X and Y are.... Pick ONE option Independent Perfectly correlated Equal to each other More than one of these choices None of these choicesSuppose X and Y are two independent random variables with: X Y mean 2 -4 st dev 3 3 The mean of X+Y is .The standard deviation of X+Y is (to two places after the decimal).In a random experiment if a coin is tossed three times or three coins are tossed one time, if random variable X is the number of appearances of Tails, the value of E(X), will be; Select one: O a. None O b. 3.5 O c. 2.5 O d. 1.5
- 3. 7 8. 10 An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth, ttt, etc. For each outcome, let R be the random variable counting the number of tails in each outcome. For example, if the outcome is tht, then R (tht)=2. Suppose that the random variable X is defined in terms of R as follows: X=R-1. The values of X are given in the table below. tth hht hth thh ttt hhh htt tht Outcome Value of X 1 - 1 1 1 Calculate the values of the probability distribution function of X, i.e. the function py. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value X of X Px (x) Submit A Continue © 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center étv MacBook Air DII DD F10 80 F9 F7 F8 F6 F4 F5 F2 F3 公 云。 olo3. An integer is randomly chosen from the set 1, 2,..., 100. If this integer is divisible by 2 we let Y = 0, and if it is not divisible by 2 but is divisible by 3 then Y = 1. We let Y = 2 in all other cases. Find mean and variance of Y.Let X1, X2, ... be a sequence of random variables with finite mean u and non-zero variance o?. Let S, = X;. Which random variable has meanequal to 0 and variance - equal to 1? Select one: S-np O a. Zn Vno Sn-H O b. Zn Vno O c. Zn Vño O d. Zn Vno
- Q.2 Listed is a series of experiments and associated random variables. In each case, identify the values that the random variable can assume and state whether the random variable is discrete or continuous. ilitu distrib blo lloweAn ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth, ttt, etc. For each outcome, let R be the random variable counting the number of heads in each outcome. For example, if the outcome is tth, then =Rtth1. Suppose that the random variable X is defined in terms of R as follows: =X−R2−3R4. The values of X are given in the table below. Outcome htt tht hth thh ttt hhh hht tth Value of X −6 −6 −6 −6 −4 −4 −6 −6 Calculate the values of the probability distribution function of X, i.e. the function p X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row.A sample of n = 20 observations is drawn from a normal population with u = 1100 and o = 180. Find each of the following: A. P(X > 1176) Probability = B. P(X 1063) Probability =
