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

Consider the theoretical cases..............

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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14. In a regression context, under what situation is the predicted value for Y equal to the mean of Y? a) when the correlation between Y and X is positive b) when the correlation between Y and X is negative c) when the correlation between Y and X is zero d) when we try to predict Y in the complete absence of X e) a and d f) c and d g) none of the above, the predicted value for Y is only equal to the mean when X is equal to 0
4. The standard deviation of X, denoted SD(X), is given by SD(X) = Var(X). Find SD(aX + b) if X has variance of o?.
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].
Z.5 points A dependent t-test study and an independent t-test study both produced a t statistic with df = 10. How many individuals participated in each study? 12 for dependent and 12 for independent 12 for the dependent and 11 for independent 11 for dependent and 11 for independent 11 for dependent and 12 for independent
7. In a sample of n= 6, five individuals all have scores of X= 10 and the sixth has a score of X=16. What is the mean for this sample?
4.2 The probability distribution of the discrete random variable X is f(x) = 3 (*)*** Find the mean of X. 3-x (¹)ª (²³)³—ª, x = 0, 1, 2, 3.
Bapu
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
2

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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 ||