2.In statistics, the mean x and variance S of a sequence ofnumbersX1, X2, X3,'are defined as:Xi(x; – x)²ni=1пi=1anduse the above definition to prove that:a) ΣT1지-치 = 0b) s² = (÷E%1x;?)– x²

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Answered: 2. In statistics, the mean x and…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Q. 47 How can you make multiple comparison in Friedman's test when H, is rejected?
A sample of ?=14n=14 observations is drawn from a normal population with ?=1030μ=1030 and ?=200σ=200. Find each of the following: A. ?(?¯>1110)P(X¯>1110) Probability = B. ?(?¯<944)P(X¯<944) Probability = C. ?(?¯>997)P(X¯>997) Probability =
7.2.3. X is the continuous uniform (-5, 5) random variable. Given the event B = {|X| < 3}, find the (a) conditional PDF, fx|B(x), (b) conditional expected value, E[X|B], (c) conditional variance, Var[X|B].
7.16 Using an app or the Web on a smartphone. The Nielsen Company reports that U.S. residents aged 18 to 34 years spend an average of 2.83 hours per day using an app or the Web on a smartphones You wonder if this it true for students at your large university because you rarely see students not using their smartphones. You collect an SRS of n = 75 students and obtain 2 = 3.17 hours with s =1.36 hours. (a) Report the 95% confidence interval for u, the average number of hours per month that students at your university use the Internet on a computer. (b) Use this interval to test whether the average time for students at your university is different from the average, reported by Nielsen. Use the 5% significance level. Summarize your results.
5.65. Find the mean µ, variance o², and standard deviation o of each distribution: 2 3 8 (a) (b) X f(x) X f(x) 1/4 -2 1/3 1/2 1/4 -1 7 1/2 1/6
4.6. Consider the following history of six events in which operations span multiple ob- jects, assuming that A and B are initialized to 0: ev = inv(write(1)) on evz = inv(sum() evy = resp(urite()) from A evA = inv(write(2)) on evs = resp(write()) from B evg = resp(sum(2)) from A, B at P at P А, В at Pa at P at P at Ps A on B Show that this history is not linearizable but normal.
4. If T follows a 17 distribution, find to such that (a) P(T| to) = .05.
Suppose X is normel with mean -10 and standard deviation 2. What is P(X>-8)? O.84 O-84 O 16 O -16
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。 olo
8. Given E(x,-)-78 and N= 80, then the population standard deviation, a, is approximately O a) 0.975 O b) 0.987 O0.994 Od) 0.110 SAMSUNG
8. The time (in minutes) that it takes a car mechanic to replace a car battery is a random variable X that follows an exponential distribution with mean 15 minutes. a) Find P(14 < X < 22). Round off your answer to two decimal places. x 22 1 P(14 < X <22) = √₂/1² 15 e 15dx = P(x < 22) — P(x < 14) x 15 122 = e 15 22 1 - e 14 or 0.8 = = 22 14 = −e 15 + e15 = 0.16254≈ 0.16 - (1 – b) Find the 80th percentile. Round off to the nearest whole number. 1 X S 15 14 e 15 t e 15 dt X 0.8 = 1 e 15 X e 15 = = 0.2 14 22 = e 15 e 15 = 0.16 x — = ln (0.2). This gives x = 24.14156 15
5.2.1 The conditional probability distribution of Y given X = x is fy.0) = xe-y for y> 0, and the marginal probability distribution of X is a continuous uniform distribution over 0 to 10. a. Graph fyv) = xe¬w for y > 0 for several values of x. Determine: b. P(Y < 2|X = 2) d. E(Y |X = x) f. fr(y) c. E(Y | X = 2) e. fxy(x, y)

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2. In statistics, the mean x and variance S of a sequence of numbers *1, X2, X3, ·… , Xn are defined as: п Xị s2 (x; – x)² n i=1 п i=1 and use the above definition to prove that: a) E1xi – i = 0 b) s² = (;E1x?) – x² i=1 ||