Let X1, X2, ... , Xn be a random sample with pdf f(x) = (0+1)xº-1, 0sx<1,
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A: Introduction: The joint density function of two random variables X and Y is given below:
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- Problem 10 : Independent random variables {U, X, W} have variances V[U] = 1, V[X] = 2, V[W] = 3.Let Y = 2U + 3X + 4W. Find the standard deviation of Y.Problem 1. A continuous random variable X is defined by f(x)=(3+x)^2/16 -3 ≤ x ≤ -1 =(6-2x^2)/16 -1 ≤ x ≤ 1 =(3-x^2)/16 -1 ≤ x ≤ 3 a)Verify that f(x) is density. b)Find the MeanProblems 5 and 6 refer to the discrete random variables X and Y whose joint distribution is given in the following table, so P(X = 1 and Y = -1) = 1/4, P(X = 1 and Y = 1) = 0, etc. Problem 5: Compute the marginal distributions of X and Y, and use these to compute E(X), E(Y), Var(X), and V ar(Y). Problem 6: Compute Cov(X, Y) and the correlation ρ for the random variables X and Y. Are X and Y independent? Y= -1 Y =0 Y =1 X =1 1/4 1/8 0 X =2 1/16 1/16 1/8 X =3 1/16 1/16 1/4
- J 1 Problem 126. Let X and Y be discrete random variables with joint probability mass function pX,Y (x, y) = C/[(x + y − 1)(x + y)(x + y + 1)], x, y = 1, 2, 3, . . . Determine the marginal mass functions of X and YQuestion 9 There are two random variables X and Y, and their correlation coefficient ρX,Y = 0.7. Now, we have two new random variables A = 2.5X+1 and B = 4Y+2. Please compute the correlation coefficient of A and B, ρA,B . Please round your answer correctly to one decimal place. Answer:_________________Problem 7: Let X be a continuous random variable with the probability density for f(x) = 3x2 values of x in [0,1], and f(x) = 0 elsewhere. Compute the expected value and variance of X.
- If two random variables X and Y are independent with marginal pdfs fx(x)= 2x, 0≤x≤1 and fy(y)= 1, 0≤y≤1 Calculate P(Y/X>2)Question 1The following table shows the number of shirts by sizes that are manufactured in a factory on aparticular week:Extra Small Small Medium Large Extra Large 390 470 520 680 440a) It was discovered that the sizing of some shirts was labelled incorrectly.(i) Give two reasons why it would be necessary to examine a sample of the shirts producedrather than examine the entire weekly production.(ii) State two differences between a cluster sample and a stratified random sample in thissituation. (iii) Using the stratified random sampling technique, calculate the number of medium shirtsthat will be selected if we require a sample of 375 shirts.13) Random variables X and Y have joint pdf fXY={4xy, 0≤x≤1, 0≤y≤1fXY={4xy, 0≤x≤1, 0≤y≤1 Find Correlation and Covariance
- Problem 2:Examine the relationship between amount of time spent studying for an exam (X) in hours andthe score that person makes on an exam (Y)X Y2 653 703 754 705 856 857 90 using spss Give the following:1. Null hypothesis2. Alternative hypothesis3. Statistical test4. Computation5. Decision6. ConclusionProblem 1. Consider the following density function. f(x )=[ (kx) ^ (2/3) * 0 < x < 2 Find the value of k. Find the cumulative distribution function ( CDF) of X Find the inverse of the CDF. Simulate a random sample of 10000 values from the above distribution by using inversetransformation and find the mean and the variance of those values, and write the Rcode.Problem 2-5.5. But change the problem to say Gaussian noise variance of 2, and threshold of 6V.
