Concept explainers
A random variable
Want to see the full answer?
Check out a sample textbook solutionChapter 12 Solutions
Pearson eText for Calculus & Its Applications -- Instant Access (Pearson+)
- Let X be the random variable having pdf f(x) = 1,0 < x < 1, zero e.w. Compute the probability of the range of the random sample of size 4 (X1, ., X4) is less than 1/2. Hint: Range is R = X(4) – X(1).arrow_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 F(x, y) = { K (x² + y²) 20 ≤ ≤ 30, 20 ≤ y ≤ 30 otherwise (a) What is the value of K? (Enter your answer as a fraction.) K= (b) What is the probability that both tires are underfilled? (Round your answer to four decimal places.) (c) What is the probability that the difference in air pressure between the two tires is at most 2 psi? (Round your answer to four decimal places.) (d) Determine the (marginal) distribution of air pressure in the right tire alone. for 20≤x≤ 30 (e) Are X and Y independent rv's? Oves, f(x, y) = fx(z) - fy (y), so X and Y are independent. Oves, f(x, y) + fx(z) - fy(y), so X and Y are independent. ONO, f(x, y) = fx(2) - fy(y), so X and Y are not independent. ONO, f(z,y) #fx(z) - fy(y), so X and Y are not independent.arrow_forwardFind the mean of random variable of X, if X is random variable with pdf f(x) = c(1-x²), -1arrow_forwardIf X has an exponential distribution, show thatP[(X Ú t + T)|(x ÚT)] = P(X Ú t)arrow_forwardLet X, and X2 be independent exponential distributions with the same parameter 2. What is the joint distribution of Y, = X, + X2 and Y, X1 -? What are the distributions of Y, and X1+X2 Y2?arrow_forwardLet X be a continuous random variable with the followirg function. Find: (a) P(2 6). * f(x) = 0. (1/8 if 0 < x <8 elsewherearrow_forwardThe random variables x, are i.i.d. and uniform in the interval (-0.5, 0.5). Show that E{(x₁ + x2 + x3)*} = 13arrow_forwardSuppose that the random variable X has the continuous uniform distribution on the interval [0,1]. A random sample of n = 36 is selected from this population. Find the probability that the sample mean is greater than 0.4 but less than 0.8.arrow_forwardplease and thank you!!!arrow_forwardA random variable X has the cumulative distribution function as below: Find its mean. F(x) = 0 x² - 2x + 2 2 Type your numeric answer and submit for x < 1 for 1 < x < 2 for x ≥ 2arrow_forwardConsider the random variable X with PDF (known as Cauchy distri- bution) f(x) = 7 - 00arrow_forwardRandom variables X and Y are connected through pgf x(s) and Vy(s) by the relation x(s) = s¥y(/s) Which of the following relationships between their means is INCORRECT?. Select one: O a. x(s) = Vy(/s) + s¥½(/s)/(2/5) O b. EX = 1+EY/2 O c. EX = 2+ 2EY O d. EY = 2 – 2EXarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill