MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Let X be an exponential random variable with standard deviation σ. Find
P(|X − E(X)| > kσ ) for k = 2, 3, 4, and compare the results to the bounds
from Chebyshev’s inequality.
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- Suppose that Y is an exponential random variable with λ = 4. Find. P[Y > (E(Y) + 2√√Var(Y))] . (round to 4 decimal points)arrow_forwardf (x) = 4xc for 0 ≤ x ≤ 1 ; Find the constant c so that f (x) is apdf of some random variable X, and then find the cdf, F (x) = P(X ≤ x). Sketch graphsof the pdf f (x) and the cdf F (x), and find the mean μ and variance σ2.arrow_forwardQ1. let Y₁ < Y₂ < Y3 < Y4 < Y5 are the order statistics of the random sample of size 5 from the distribution : f(x) = 3x², 0arrow_forwardA random variable, X, has a pdf given by The expected value of Y is O a. 3/5 O b. 5/3 O c. 7/5 O A random variable Y, is related to X by Px(x) d. 7/3 = 1 -3 < x < 1. and 0 otherwise 4 Y = X²arrow_forwardA random sample of size n₁ = 14 is selected from a normal population with a mean of 76 and a standard deviation of 7. A second random sample of size n₂ = 9 is taken from another normal population with mean 71 and standard deviation 11. Let X₁ and X₂ be the two sample means. Find: (a) The probability that X₁ – X₂ exceeds 4. 1 2 (b) The probability that 4.3 ≤ X₁ – X2 ≤ 5.6. Round your answers to two decimal places (e.g. 98.76). (a) i (b) iarrow_forward3. Suppose X is a discrete random variable with pmf defined as p(x) = log10 ( for %3D x = {1,2,3,...9} Prove that p(x) is a legitimate pmf.arrow_forwardarrow_back_iosarrow_forward_ios
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