3. The joint pdf of random variables X and Y is given by fxx(x, y) = {k (x² + 3 y), 0, -1 ≤ x ≤ 1,0 ≤ y ≤ 1 − x² otherwise (a) Find k. (b) Find P[0≤ X ≤ 1/2] (c) Find P[Y X + 1].
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![3. The joint pdf of random variables X and Y is given by
fxx(x, y) = {k (x² + 3
y),
0,
-1 ≤ x ≤ 1,0 ≤ y ≤ 1 − x²
otherwise
(a) Find k.
(b) Find P[0≤ X ≤ 1/2]
(c) Find P[Y X + 1].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F97354b51-6511-4dc6-9828-a30de53b85ca%2Fe64bde7b-606c-4a56-b04c-c42ed7126ddb%2Fgez8dv7_processed.jpeg&w=3840&q=75)
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Solved in 2 steps
- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.3. Let X be a continuous random variable on the interval [0, 1] having cdf Fx(x) = 3x² − 2x³. Let W = 4 + 3X. (a) What is the range of W? (b) Find a formula for Fw(w). (c) Find a formula for fw(w).Let the joint pdf of random variables X,Y be fx,y (x, y) = a(x + y)e-2-Y, for all æ > 0, y 2 0. Find the conditional pdf Tylx (y|x) = &x2) fx(x)
- Let Y be a continuous random variable with √ ½ (2 f(y) = = Find the mean (u) and variance (o²) of Y. (2−y), 0≤ y ≤ 2 elsewhere.B) Let the random variable X have the moment generating function e3t M(t) for -1Suppose X is a random variable, whose pdf is defined as follows: 2x = (²x) (u(x) - u(x − 3)) where u(x) is the unit step function. Determine the conditional pdf fx(x 1. Let Y be a continuous random variable where f(y) F(y)? (a) Y 18 Y 15 Y-3 18 Y+3 (b) (c) (d) 18 (e) None of the above = 1 18 -3 ≤ y ≤ 15. What is8. (Same as #4) At a particular gas station, gasoline is stocked in a bulk tank each week. Let random variable X denote the proportion of the tank's capacity that is stocked in a given week, and let y denote the proportion of the tank's capacity that is sold in the same week. The joint pdf of X and Y is given by f(x,y) (3x if 0 ≤ y < x < 1 = 0 otherwise a) Find the marginal probability distributions of X and Y. b) Show that the two random variables are not independent. Using part of your answer to a) is a much shorter solution. Once you've done this with probability, using common sense is VERY straightforward.Let X be a random variable such that E(X²) a. V(3X-3) b. E(3x-3) = 58 and V(X) = 40. ComputeSuppose that X₁, X2, X3 are independent and identically distributed random variables with distribution function: Fx (x) = 1 – 3¯ª for x ≥ 0 and Fx (x) = 0 for x 1).Suppose Y1 and Y2 are random variables with joint pdf (6(1 — у2), 0, 0 < y1 < y2 fv, otherwise Y1 Let U1 and U2 = Y,. Use the transformation technique to show that U, follows a uniform Y2 distribution from 0 to 1.(f) Find (g) Find E(X1X2 – X3). Let Z1 and Z2 be two independent N(0, 1) random variables. Derive the distribution of Y = 50+ 3Z1 + 4Z2. Let X1, X2, ..., Xn be a random sample from the population N(u, 02) and Y1, Y2,... ,Y,m a random g2) where hoth means (Um and ln.) are assumed known. Note thatSEE MORE QUESTIONSRecommended textbooks for youAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
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