b)Let X₁, X₂,..., X5 be a random sample of size 5 from the standard normally population. If thestatistic Y is given byY =X1 X2 X3√√X₁²+X3²+X5²²i) Briefly explain why Y follows a Student's t distribution with 3 degrees of freedom.ii) Compute the probability that Y is between 2.35 and 5.84.iii) What is the mean and variance of the statistic Y?QUESTION O

Answered: b) Let X₁, X₂, ..., X5 be a random…

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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x; Let be a random variable from the normal distribution with 8 means, 16 variances.Let's select a subset of 25 elements from the main massthe mean of these subsets MUST BE BETWEEN 7 and 10.
8) a) In simple words describe the median, dos, of the probability distribution for a continuous random variable Y. b) Write the median for a random variable with uniform distribution on the interval [a,b]. c) Write the median for a normal distribution with mean u and standard deviation o. d) Find the median for an exponential distribution with mean ß.
The weights of beagles (dogs) have approximately a normal distribution with u = 17.1 pounds and a standard deviation of o = 1.8 pounds. Suppose that we randomly select n = 64 beagles and measure their weights in pounds. Let X be the random variable representing the mean weight of the selected beagles. Let Xtot be the random variable representing the total weight of the selected beagles. a) About what proportion of beagles have weights between 17 and 18 pounds? b) About what proportion of beagles have weights greater 20 pounds? c) About how many of the 64 sampled beagles have weights less than 16.5 pounds? (nearest integer) d) About how many of the sampled beagles have weights between 17 and 18 pounds? (nearest integer) e) What is the standard deviation of the distribution of X? f) What is the standard deviation of the distribution of Xtot? g) What is the probability that 17 1100? f) Copy your R script for the above into the text box here.
Assume a normally distributed population of resting heart rates with μ = 76 and σ = 5. Compute the z-score for a heart rate of 73. What is the probability of randomly selecting someone whose heart rate is below 73? What is the probability of randomly selecting someone whose heart rate above 79? What is the probability of randomly selecting someone whose heart rate either below 60 or above 90?
4. Suppose that 60% of college students own a smart phone manufactured by Apple. If a random sample of 200 college students is selected, use the normal distribution to approximate the probability that the number of students in the sample owning a smartphone made by Apple will be less than 105. Is it reasonable to use the normal approximation here?
8) A normal random variable x has an unknown mean and the standard deviation. The probability that X exceeds 4 is 0.9772, and The probability that X exceeds 5 is 0.9332. Find u and o.
3. Let X be the mean of a random sample of n = 25 from the distribution with a mean of 30 and a variance of 9. Find an approximated probability that the sample mean is between 29.8 and 30.6.
3. The taxi and takeoff time for commercial jets is a random variable x with a mean of 8 minutes and a standard deviation of 3 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. a). Find the probability that for 36 jets the average taxi and takeoff time is less than 8.33 minutes per plane. b). Find the probability that for 36 jets the average taxi and takeoff times is more than 8.55 minutes.
24. Show that the mean x of a random sample of size n from the distribution : 1 f (x, €) =e, 0 0 x/e e? is the M.L.E. of 0 with variance
Total blood volume (in mi) per body wight (in ke) is important in medical research. For healthy aduks, the red blood cell volume mean is about p = 28 ml/kg.t Red blood cell vokume that is too lom ar too high can indicate a medical problem. Suppose that koger has had seven blood tests, and the red blood cell volumes weré as follows Let x be a random variable that represents Roger's red blood cll volume. Assume that x has a narmal distributian and - 4.75. Do the data indicate that koger's red blood cell valume is different (either way) from a- 28 mi/kg? Use a 0.01 lervel of significance. a What is the leval of sigaicance State the null and alternate hypotheses. Will you use a left-lailed, right-laded, or two-tailed test? O H: - 28 ml/kg; H: 2s m/kg; Ima-tailed o Ho: - 28 ml/ka; H 28 m/ka, let-tailed O Ho: 28 mil/kg: H1:- 28 ml/kg; tmo-tailed O Ho: 28 m/ka, H > 28 m/kg; right-laiked (b) What sampling distribution wil you use? Explain the rationale for your choice of sampling distributian.…

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