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Problem 3 Suppose that we have a random variable with pdf given by f(1) = exp(-2)...
4. Let X have the following PDF: sin(x) , 0 < x < π , otherwise...
4. Let X have the following PDF: sin(x) , 0 < x < π , otherwise Ix(x) = 0 Find the CDF of X Using the Probability Integral Transformation Theorem, describe the process of generating values from the density of X Using R, generate 1,000 values using your process in part b. Produce a histogram of these generated values, and overlay the density curve of X over top. (Hint: in R, the function acos calculates the inverse cosine function.) Using...
(25 pts.) Let the random variable X have pdf f(x) = { 0<x<1 1<isa Generate a...
(25 pts.) Let the random variable X have pdf f(x) = { 0<x<1 1<isa Generate a random variable from f(x) using (a) The inverse-transform method (b) The accept-reject method, using the proposal density 9(x) = 0sos
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given...
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given by f(x) - 3x2; 0< x < 1, - 0; otherwise Find the cumulative distribution function (i.e., cdf) of Y = X3 first and then use it to find the pdf of Y, E(Y) and V(Y)
2. Let X ~ Exp(B), i.e. it is an exponential random variable with parameter 8. Find...
2. Let X ~ Exp(B), i.e. it is an exponential random variable with parameter 8. Find F(x) (the cdf) and F-16) (the inverse of the cdf).
[25 points] Problem 4 - CDF Inversion Sampling ers coming from the U(0, 1) distribution into...
[25 points] Problem 4 - CDF Inversion Sampling ers coming from the U(0, 1) distribution into In notebook 12, we looked at one method many pieces of statistical software use to turn pseudorandom those with a normal distribution. In this problem we examine another such method. a) Simulating an Exponential i) The exponential distribution has pdf f(x) = le-ix for x > 0. Use the following markdown cell to compute by hand the cdf of the exponential. ii) The cdf...
1. Let X be a random variable with pdf f(x )-, 0 < x < 2-...
1. Let X be a random variable with pdf f(x )-, 0 < x < 2- a) Find the cdf F(x) b) Find the mean ofX.v c) Find the variance of X. d) Find F (1.75) e) Find PG < x < +' f) Find P(X> 1). g) Find the 40th percentile.*
19. A random variable X has the pdf f(x) = 2/3 0 otherwise if 1 <...
19. A random variable X has the pdf f(x) = 2/3 0 otherwise if 1 < x 2 (a) Find the median of X. (b) Sketch the graph of the CDF and show the position of the median on the graph.
(1) Suppose the pdf of a random variable X is 0, otherwise. (a) Find P(2 <...
(1) Suppose the pdf of a random variable X is 0, otherwise. (a) Find P(2 < X < 3). (b) Find P(X < 1). (e) Find t such that P(X <t) = (d) After the value of X has been observed, let y be the integer closest to X. Find the PMF of the random variable y U (2) Suppose for constants n E R and c > 0, we have the function cr" ifa > 1 0, otherwise (a)...
Develop a generator for a random variable whose pdf is F(x) ={ 1/3, 0<=x<=2 1/24, 2<x<=10...
Develop a generator for a random variable whose pdf is F(x) ={ 1/3, 0<=x<=2 1/24, 2<x<=10 0, otherwise a) Write a computer routine to generate 1000 values. b) Plot a histogram of 1000 generated values. c) Perform goodness-of-fit test to determine whether these generated values fits the theoretical density function given above. Note: Invlude your computer routine for generating random variates in your answer sheet. I need numerical solution
Question 3 Suppose that the random variable X has the following prob- ability density function. f(x)...
Question 3 Suppose that the random variable X has the following prob- ability density function. f(x) =1- for 1 € (0,2), and zero otherwise. a) Plot the graph of the pdf of x. b) Is it true that Pr[X <0] = 0.5? c) Is it true that Pr[X < 1] = 1? d) Is it true that E[X] < 0.5? e) Is it true that Prix < 0.5) > 0.5? f) Find the CDF of x. Compare the graph of...
4. Let X have the following PDF: sin(x) , 0 < x < π , otherwise Ix(x) = 0 Find the CDF of X Using the Probability Integral Transformation Theorem, describe the process of generating values from the density of X Using R, generate 1,000 values using your process in part b. Produce a histogram of these generated values, and overlay the density curve of X over top. (Hint: in R, the function acos calculates the inverse cosine function.) Using...
(25 pts.) Let the random variable X have pdf f(x) = { 0<x<1 1<isa Generate a random variable from f(x) using (a) The inverse-transform method (b) The accept-reject method, using the proposal density 9(x) = 0sos
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given by f(x) - 3x2; 0< x < 1, - 0; otherwise Find the cumulative distribution function (i.e., cdf) of Y = X3 first and then use it to find the pdf of Y, E(Y) and V(Y)
2. Let X ~ Exp(B), i.e. it is an exponential random variable with parameter 8. Find F(x) (the cdf) and F-16) (the inverse of the cdf).
[25 points] Problem 4 - CDF Inversion Sampling ers coming from the U(0, 1) distribution into In notebook 12, we looked at one method many pieces of statistical software use to turn pseudorandom those with a normal distribution. In this problem we examine another such method. a) Simulating an Exponential i) The exponential distribution has pdf f(x) = le-ix for x > 0. Use the following markdown cell to compute by hand the cdf of the exponential. ii) The cdf...
1. Let X be a random variable with pdf f(x )-, 0 < x < 2- a) Find the cdf F(x) b) Find the mean ofX.v c) Find the variance of X. d) Find F (1.75) e) Find PG < x < +' f) Find P(X> 1). g) Find the 40th percentile.*
19. A random variable X has the pdf f(x) = 2/3 0 otherwise if 1 < x 2 (a) Find the median of X. (b) Sketch the graph of the CDF and show the position of the median on the graph.
(1) Suppose the pdf of a random variable X is 0, otherwise. (a) Find P(2 < X < 3). (b) Find P(X < 1). (e) Find t such that P(X <t) = (d) After the value of X has been observed, let y be the integer closest to X. Find the PMF of the random variable y U (2) Suppose for constants n E R and c > 0, we have the function cr" ifa > 1 0, otherwise (a)...
Question 3 Suppose that the random variable X has the following prob- ability density function. f(x) =1- for 1 € (0,2), and zero otherwise. a) Plot the graph of the pdf of x. b) Is it true that Pr[X <0] = 0.5? c) Is it true that Pr[X < 1] = 1? d) Is it true that E[X] < 0.5? e) Is it true that Prix < 0.5) > 0.5? f) Find the CDF of x. Compare the graph of...
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