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Find the expected values and the standard deviations (by inspection) of the normal random variables with the density functions given in Exercises 15–18.
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Calculus & Its Applications (14th Edition)
- Part III: Sections 3.1- 3.3 13. Suppose that X is a continuous random variable with pdf given as 43 if 1< <4 255 f(1) = %3D otherwise. (a) For 1arrow_forward(Math 161A/163 review) Suppose that X₁, X2, X3 are independent Exponential (A) random variables. A> 0 and r> 0 are constants. Find the mean and variance of Y where Y = 2(X₁+rX2 - X3)arrow_forwardIdentify the distributions of the random variables with the moment- generating functions shown below. For each random variable also indicate what the mean and the variance are. a) m(t) = e22(e'–1) b) m(t) = 1/(1 – 2t)² %3D с) т() — 4t d) m(t) = (0.3e + 0.7)18arrow_forwardLet X be a random variable such that E(X²) a. V(3X-3) b. E(3x-3) = 58 and V(X) = 40. Computearrow_forwardPart II: Sections 2.1 - 2.7 8. Assume that X is a geometric random variable with p=0.32. (a) Compute P(X > 13[X > 3). (b) Compute E(X²).arrow_forwardb. Find E[X(X – 1)] for Poisson random variable. Use the result to find the variance of X.arrow_forwardA random variable Y has a uniform distribution over the interval (?1, ?2). Derive the variance of Y. Find E(Y)2 in terms of (?1, ?2). E(Y)2 = Find E(Y2) in terms of (?1, ?2). E(Y2) = Find V(Y) in terms of (?1, ?2). V(Y) =arrow_forwardExercise 3. Let X be a random variable with mean µ and variance o². For a € R, consider the expectation E((X − a)²). a) Write E((X - a)²) in terms of a, μ and σ². b) For which value a is E((X − a)²) minimal? c) For the value a from part (b), what is E((X − a)²)?arrow_forwardLet X ∼ U(a, b). Use the definition of the variance of a continuous random variable (Equation 2.38 or 2.39) to show that . σ²X = (b-a)²/12.arrow_forward1.4 Let X be a continuous random variable with pdf, fx(x), and fx(t+5) = fx(5 – t) for all t> 0. Please provide the mean of X.arrow_forward3. Let X be an exponentially distributed random variable with parameter 2. a) Find and sketch the cdf and pdf of Y = 2- 3X. b) Find the mean and variance of Y. c) Find the distribution of Z = VX. Calculate its mean and variance in Mathematica. d) Obtain characteristic functions of X and Y.arrow_forwardB) Let the random variable X have the moment generating function e3t M(t) for -1arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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