The density function of X is given by f(x): and b. (a + bx² = 0 otherwise 0≤x≤1. If E[X]=, find a 40 If X1, X2,...,X40 are independent random variables with means μ₁ = µ₂ = ... = μ40 = 1, and variances σ = σ = = σ40 = 1, and if Y = 5X₁ - 3X₂+X3 +43X₁, what are the mean and variance of Y?
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![The density function of X is given by f(x):
and b.
(a + bx²
=
0
otherwise
0≤x≤1. If E[X]=, find a](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb9e27b5d-0ab8-428e-954d-97d64fc14c61%2Fdf14849b-c1b3-4345-ab2b-aabdf83364d2%2Fqio07d_processed.png&w=3840&q=75)
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- The density function of X is given by f(x) = = (a + bx2, 0 ≤x≤1 0, elsewhere If E = [x] = = find a, bDetermine whether f(x) is a probability density function on the interval [0, 4]. If not, determine the value of the definite integral. f(x) = 3x² 256If x has a uniform density with a=-2 and b=5. Let y=|x|. Find the probability density function of y , use g(y). What is p(y
- If the probability density of X is given by f(x)=6x(1–x) 0Let f(x) = k(4x –x²) if 03. (a) For what value of k is f(x) a probability density function? (b) For that value of k, find P (x>2). (c) Find the mean.A VA X has a probability density f (x) = 3x² in the interval [0.1]. Determine F (x) = p (xLet X denote 0.025 × the ambient air temperature (˚C) and let Y denote the time (min) that it takes for a diesel engine to warm up. Assume that (X, Y) has joint probability density function f(x,y) = 1.6x (1 − x)(6 + 5x − 4y), for 0 < x < 1, 0 < y < 0.5. Find the regression curve for X as a function of warm-up time Y = y and plot it. Use it to predict the air temperature = 40X for warm up time Y = 0.25 min.Suppose that X and Y have the following joint probability density function.f (x, y) = 3x 400 0 < x < 6, y > 0, x − 4 < y < x + 4 (a) Find E(XY). (b) Find the covariance between X and Y.Suppose that X and Y have the following joint probability density function. f(x,y) = 134² 0 0, x − 2 < y < x+2 (a) Find E(XY). (b) Find the covariance between X and Y.The conditional probability density function of Y, given that X=x for some x>0, takes the following form: fyx=x(y) = C (x²-y²) x° e Ex, for -xSuppose Z = X +Y. Give the probability density value at z = 0, fz(0). fx(x) fy(y) 1/2 1/2 -1 y. Find the expected value of the Probability density function: ƒ(x)= 24 (3x)(4 — x) - 64 on the interval of [0,4]. Then find V(x), and oSEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON