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Chapter 10 Solutions
A First Course in Probability
- Explain the differences between Gaussian elimination and Gauss-Jordan elimination.arrow_forwardSuppose that X, and X2 are aiscrete random variables with joint pdf of the form f(x1, x2) = c(x, + x2), x1 = 0,1,2; x2 = 0,1,2arrow_forwardSuppose a continuous random variable X has the following CDF:: F(x) = 1 - 1/ (x+1)4, x > 0.Find SX (x), survival function? a 1/(x+1)4, x < 0 b -1/(x+1)4, x > 0 c (x+1)4, x > 0 d 1/(x+1)4, x > 0arrow_forward
- Suppose that X1, X2, and X3 are independent and identically distributed continuous random variables with common density function f(x). (a) Compute P(X1 > X2) (b) Compute P(X1 > X2j X1 > X3) (c) Compute P(X1 > X2| X1 < X2) Hint: You can answer this problem easily using symmetry.arrow_forwardLet X be a random variable and a real number. Show that E(X - a)² = varX + (µ − a)² Hereμ = EX is the expected value of the random variable X and varX = E(X - μ)^2 is the variance of the random variable X. Guidance: start from the representation - (X-a)^2 = (X µ + μ- a)^2 and group the right side of the representation appropriately into the form (Z + b)^2, where Z is some random variable and b is a real number and open the square. The task should be solved with the help of the expected value calculation rules.arrow_forwardLet X and Y be random variables with variances Var(X) = 1 and Var(Y ) = 2. (Note that X and Y might not be independent.) What is the maximum possible value of Var(3X − 2Y + 4)?arrow_forward
- Suppose that X1, X2, X3 are independent and identically distributed random variables with distribution function: Fx (x) = 1 – 2 for x >0 and Fx (x) = 0 for x 1).arrow_forwardLet fix) = 2x, 0arrow_forwardSuppose that X₁, X2, X3 are independent and identically distributed random variables with distribution function: Fx (x)=12* for x ≥ 0 and Fx (x) = 0 for x 4).arrow_forwardLet X1, X2,... , Xn be independent Exp(A) random variables. Let Y = X(1)min{X1, X2, ... , Xn}. Show that Y follows Exp(nA) dis- tribution. Hint: Find the pdf of Yarrow_forwardEach front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose the actual air pressure in each tire is a random variable-X for the right tire and Y for the left tire, with joint pdf given below. (x²+ y2) 21 ≤ x ≤ 32, 21 ≤ y ≤ 32 f(x, y) = x) = {K(x² + y²) otherwise (a) Compute the covariance between X and Y. (Round your answer to four decimal places.) Cov(X, Y) (b) Compute the correlation coefficient p for this X and Y. (Round your answer to four decimal places.) p =arrow_forwardLet X = (X1, X, )" be a bivariate random variable with variance-covariance matrix 4 -1.5 E(X – E(X))(X – E(X))") = ( -1.5 1 You are given that X1 + aX2 is independent of X1. Find the number a. Give your answer in 2 decimal places. Answer:arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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