13. Generate a sample of size n = 100 from a chi-square distribution with 5 degrees of freedom. Plot the density of f and the estimate f(-) given in (11.2.6) based on (a) № (0, 1) kernel and bandwidth 1.06n¯½ s based on a N(0, 1) reference distribution. (b) U[−1, 1] kernel and h = 1.95n¯½ s based on a N(0, 1) reference disribution.
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![13. Generate a sample of size n = 100 from a chi-square distribution with 5 degrees of
freedom. Plot the density of f and the estimate fħ(•) given in (11.2.6) based on
(a) √(0, 1) kernel and bandwidth 1.06n-&s based on a N(0, 1) reference distribution.
(b) U[−1, 1] kernel and h = 1.95n¯½ s based on a N (0, 1) reference disribution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66f52ea3-13fd-4902-bc86-2f48a4cfbf0d%2F6b934572-6795-4c10-8442-1a9b9148abb6%2Ftxc7vtq_processed.png&w=3840&q=75)
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- z =(x-µ)/σ = (30-29)/2.45 = 0.4082Probability P(z) = NORMSDIST(0.4082) = 0.6585 or 65.85% How is 0.4082 changed to o.6585?3. Fit a least squares quadratic curve to the following data and estimate Y at X = 2.4 fig. 03 2 3. 4. గోలిగౌజి రర్ Y 1.7 1.8 2.3 2.3 A. The required least squares quadratic curve(parabola) and the estimated value of Y at X=2.4? * 大 O Y= 2- 0.5X + 0.2X^2; Y = 1.952 Y= 2-0.6X+ 0.2X^2; Y = 1.712 O Y= 2.1 - 0.5X + 0.2X^2;Y = 2.052 Y= 2- 0.5X + 0.4X^2; Y = 3.1044. The annual precipitation X in a city is modeled by a normal distribution with a mean value of ux = 125 cm and a coefficient of variation of 8g = 0.2. Determine the following: а) Р(100 стLet X and Y be independent Exp(2) random variables. Define W = X + Y. a) Determine the correlation between X and W. The joint pdf of X and W is: fx,w(x, w) = 1^(2) e^(-1w) I{OX1,X2,...,Xn are i.i.d. random variables from N(0,θ) distribution. Here, θ= σ2 >0is the variance of the distribution, and is an unknown parameter. Find the MLE of θ(no need tocalculate the second derivative).Once an individual has been infected with a certain disease, let X represent the time (days) that elapses before the individual becomes infectious. An article proposes a Weibull distribution with a = 2.6, B = 1.8, and y = 0.5. [Hint: The two-parameter Weibull distribution can be generalized by introducing a third parameter y, called a threshold or location parameter: replace x in the equation below, a -x« – le-(x/B)ª Ba x 2 0 f(x; а, B) %3D x y.] (a) Calculate P(1 1.5). (Round your answer to four decimal places.) 0.8050 (c) What is the 90th percentile of the distribution? (Round your answer to three decimal places.) 2.980 |× days (d) What are the mean and standard deviation of X? (Round your answers to three decimal places.) 1.594 х days mean standard deviation 0.585 X daysa) X is a normally distributed variable with mean u = 30 and standard deviation o = 4. Find i) P(x 21) iii) P(30Need help with parts C & D The proportion of Americans who have frequent migraines is 15.2% according to the CDC. An acupuncturist claims that her treatment can reduce this figure significantly. A random sample of 191 Americans is administered the acupuncturists treatment and 25 report experiencing migraines.a. State Hypotheses to the scenario using the correct symbols. b. What is the sample proportion? (Round to 2 decimal places) ˆpp^= c. Suppose the P-value is calculated to be 0.0318What would your decision be for this test using α=α= 0.025? fail to reject the null accept the null reject the null d. Write a conclusion in terms of the acupuncturist's claim. Use the model provided by the instructor. Assume no errors were made.Let s be the sample variance of a random sample of size n1 fron a Normal(41,o²) population and s, be the sample variance of a random sample of size 12 from a Nornal(µ2,0²) population and the two samples are independent. Note that the two samples have the same population variance o² but µi # j12 and n1 # 12. Define the pooled variance estimator as (n1 – 1)sỉ + (n12 – 1)s3 T1 + n2 - 2 -- Is s? unbiased for o2 ? Explain with precisc computation. Find the distribution of ºP. Give the reasoning of your answer. Find the variance of s.2.Suppose that the return R (in dollars per share) of a stock has the uniform distribution on the interval [-3,7]. Suppose also, that each share of the stock costs $1.50. Let Y be the net return (total return minus cost) on an investment of 10 shares of the stocks. Compute E(Y).5. Assume you are shooting at a target centred at the origin (0,0), but bullets land at a random point with horizontal (X) and vertical (Y) coordinates following in- dependent standard Normal (0,1) distributions. Define the distance from the tar- get to be D = VX²+Y². For independent standard Normals, we already know that X? - x²(1) = Gamma(1/2,1/2) and X² + Y² ~ x²(2) = Gamma(1, 1/2). Y /D %3D (a) Find the probability that a bullet lands in the top right quadrant. (Hint: You don't need to calculate any integrals.) (b) Find the conditional probability that a bullet lands more than 1 unit away from the centre (D > 1), given Y = X, i.e. the bullet lands on the identity line; express the probability as a function of the standard Normal CDF ¤(·). (c) Find the CDF of X² + Y² in closed form. (d) Find the probability that a bullet lands more than 1 unit away from the centre, P(D> 1). (e) Find the CDF of D based on the CDF of X? + Y². (f) Use your answer in the previous part to find the PDF of…6. Suppose you walk a hiking trail at a speed which is uniformly distributed from 4 to 6 miles per hour. The distance of the trail is 24 miles. Find the PDF of the duration of the trip. (Note: speed = distance/time)Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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