3.5.2. Let X and Y have a bivariate normal distribution with parameters u1 =3, 42 = 1, of = 16, o = 25, and p = . Using R, determine the followingprobabilities:%3|(a) P(3 < Y < 8).(b) P(3 < Y < 8|X = 7).(c) P(-3 < X < 3).(d)P(-3< X < 3|Y = -4).

Answered: 3.5.2. Let X and Y have a bivariate…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Problem 1P

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Suppose, household color TVs are replaced at an average age of μ = 9.0 years after purchase, and the (95% of data) range was from 5.8 to 12.2 years. Thus, the range was 12.2 − 5.8 = 6.4 years. Let x be the age (in years) at which a color TV is replaced. Assume that x has a distribution that is approximately normal. (a) The empirical rule indicates that for a symmetric and bell-shaped distribution, approximately 95% of the data lies within two standard deviations of the mean. Therefore, a 95% range of data values extending from μ − 2σ to μ + 2σ is often used for "commonly occurring" data values. Note that the interval from μ − 2σ to μ + 2σ is 4σ in length. This leads to a "rule of thumb" for estimating the standard deviation from a 95% range of data values. Estimating the standard deviationFor a symmetric, bell-shaped distribution, standard deviation ≈ range 4 ≈ high value − low value 4 where it is estimated that about 95% of the commonly occurring data…
Take a=1 in the question
7. Assume that X and Y have a bivariate normal distribution having means 14.l and 1.3, and standard deviations 2.5 and 0.1, respectively, with correlation coefficient 0.8. Find P(Y >1.4|X =15) and P(X >15|Y = 1.4).
16. Let X, X2 X, be a random sample from a normal distribution, X, N(6, 25), and denote by X and S2 the sample mean and sample variance. Use tables from Appendix C to find each of the following: (a) P[3 < X < T. (b) P[L860< 3(X-6)/S]. (c) PIS <319375]
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Reaction time is the amount of time it takes to respond to a stimulus, and for automobile drivers, it is an important factor in staying safe while on the road by avoiding rear-end collisions. Reaction times vary from driver to driver and tend to be longer than one might think. A recent study determined that the time for an in-traffic driver to react to a brake signal from standard brake lights can be modeled with a normal distribution having mean value 1.24 seconds and standard deviation of 0.45 seconds. If we let X denote reaction time for automobile drivers, use the appropriate Normal Distribution to determine each of the following. 1. What is the probability that a driver has a reaction time less than 0.6 seconds? 2. Approximately what proportion of drivers have a reaction time more than 2.5 seconds? 3. Within what limits, centered about the mean, would you expect driver reaction times to lie with 95% probability? What are the z-scores for these limits? 4. What is the reaction time…
Q.4-52
roblem 1 If the population parameters are μ = 7 and σ = 1: a) Compute the z score for the lowest (x-4) and highest grade (x=10). (15 pts) -3 b) Compute the proportion of the normal distribution corresponds to z-score values greater than the highest grade. (10 pts) 7 = 7 0 σ = I X = 10 3 3.00
3.4 Solve the below problem: Let Y, and Y, have a bivariate normal distribution: 2. 1. 2. Y2-H2 exp 2no,02y1-p2 2(1-p2) {. (ज-र.) + ( ज-र) (ज-पदर) 07 (जब)} Dr= –00 < y, < ∞, -00 < y2 < ∞, Show that the marginal distribution of Y, is normal with mean µz and variance o is given by: 2, 1 f(y2) = 203 ,-00 < Y2 < ∞ 2.
Example 9-4. X is a normal variate with mean 30 and S.D. 5. Find the probabilities (i) 26 45, and (iii) |X – 30l > 5.

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3.5.2. Let X and Y have a bivariate normal distribution with parameters µ1 3, p2 = 1, of = 16, o = 25, and p = . Using R, determine the following probabilities: (a) P(3