RStudio code. Approximate the following intervals using random samples from a uniform distribution: (a) So the-z*/2dx....
USING MATLAB PLEASE PROVIDE THE CODE. THANK YOU
1s an exponential random variable with rate parameter 2. 1. Assume (1) Generate 1000 samples from this exponential distribution using inverse transform method (2) Compare the histogram of your samples with the true density of Y
1s an exponential random variable with rate parameter 2. 1. Assume (1) Generate 1000 samples from this exponential distribution using inverse transform method (2) Compare the histogram of your samples with the true density of Y
Let Xn = a sin(bn+Z), where n ∈ Z, a, b ∈ [0, ∞) are constant,
and Z has a continuous uniform distribution on [−π, π] (i.e. Z ∼
U([−π, π])). Show that Xn is stationary. (Hint: sin(x) sin(y) = 1 2
(cos(x − y) − cos(x + y)) may be helpful).
l. Let Xn-a sin(bn+ Z), where n є z, a, b є lo,00) are constant, and Z has a continuous uniform distribution on [-π, π] (i.e. Z ~...
the random variables x y and z have uniform continuous distribution on the region x^2 + y^2 +z^2 <= 16 a) find the (constant) value of the dennsity of that dsitribution b) determine P(x^2 + y^2 + z^2 >=4) c) determine P(x^2 + y^2 + z^2 <= 25) d) P(x > 0)
---------------- TO BE COMPLETED USING RSTUDIO------------------ Use the approximate value for the degrees of freedom (the smallest between ?1 − 1 and ?2 − 1). Random samples of resting heart rates are taken from two groups. Population 1 exercises regularly, and population 2 does not. The data from these two samples (in beats per minute) are given below: Exercise group (sample from population 1): 65.6, 67.5, 59.9, 70.6, 62.4, 64.9, 63.3, 66.3, 62, 69.5 No exercise group (sample from population...
, Samples In 30) drawn from a uniform distribution la Minitab was used to generate the samples. es 300, b 500) Variables 15 Observations Variable TypeFormValues Missing Sample 1 Quantitative Sample 2 Quantitative Numeric Sample 3 Quantitative Numeric Sample 4 Quantitative Sample 5 ive Sample 6 Quantitative Sample 7 Quantitative Observations Sample 8 Quantitative Numeric Sample 9 Quantitative Sample 10 Quantitative Sample 11 Quantitative Sample 12 Quantitative Sample 13 Quantitative Sample 14 Quantitative Sample 15 Quantitative Numeric Numeric Variable Numeric...
Probability
5. The discrete random variable Z has the following probability distribution 2 0.2 4 P(Z) 0.1 0.25 0.05 0.3 Which of the following is FALSE? A) P(Z < 2) 0.55 B) P(Z 2 4)- 0.45 C) P(Z 4)=0.9 D) P(Z3)-0.05 6. A random sample of 100 first-year students was selected to determine the average GPA they achieved at a university. A 95% confidence interval for the average GPA of the first-year students was 5.2 < H < 6.8 based...
7.70. Let X,...,x,; Y,., Y,; Z,..,Z, be respective independent random samples from three normal distributions N(u,a+ B, a) N(4-B+y,a), N(= a + y , a'). Find a point estimator for B that is based on X, Y, Z. Is this estimator unique? Why? If a is unknown, explain how to find a confidence interval for B.
7.70. Let X,...,x,; Y,., Y,; Z,..,Z, be respective independent random samples from three normal distributions N(u,a+ B, a) N(4-B+y,a), N(= a + y ,...
(5 pts) Let U be a random variable following a uniform distribution on the interval [0,1 Let Calculate analytically the variance of X. (HINT: E g(x)f(x)dx, and the p.d.f. 10SzSI 0 o.t.w. f(x) of a uniform distribution is f(x) =
(5 pts) Let U be a random variable following a uniform distribution on the interval [0, 1]. Let X=2U + 1 Calculate analytically the variance of X. (HINT : Elg(z)- g(z)f(x)dr, and the pdf. 0 < z < 1 0 o.t.w. f(x) of a uniform distribution is f(x) =
Confidence Level Question 1 One hundred random samples, each of size 25, are obtained from the Normal distribution with mean 0 and standard deviation 1 using Minitab. Subsequently, the 1-Sample Z procedure in Minitab is used (with the same confidence level) to obtain a confidence interval from each sample. Out of the 100 intervals thus obtained, 89 include the number 0. Estimate the confidence level (in percentage terms) used to generate the 100 intervals using a 95% confidence interval. a....