For random variables X, Y with joint distribution function 3x² siny 0≤ x ≤ 1,0≤ y ≤ 1 f(x,y) = Compute the marginal distribution of X.
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- Suppose X = 1/(1+Y), where 3 Y ~ fy(y) = 12 1+y y > 0, 0, otherwise. Identify the distribution of X by name and parameter values.Let Y > 0 be a continuous random variable representing time from regimen start to bone-marrow transplant. Everyone does not survive long enough to get the transplant. Let X > 0 be a continuous random variable representing time from regimen start to death. We can assume X ⊥ Y and model time to death as X ∼ Exp(rate = θ) and time to transplant as Y ∼ Exp(rate = µ). Where Exp(rate = λ) denotes the exponential distribution with density f(z | λ) = λe−λz for z > 0 and 0 elsewhere - with λ > 0. Find the probability that the patient would die before receiving transplant.If the random variable X has uniform distribution on the interval [0, a], what is the probabilitythat the random variable greater than its square, that is P (X > X^2)?
- Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose the actual air pressure of the right and left tires are random variables X and Y respectively, with the joint p.d.f. f(x, y) = K(x^2+ y^2) when 20 < X < 30 and 20 < y < 30 and zero otherwise. Determine the marginal distribution of air pressure in the right tire alone. (Leave it in terms of K)2) Let X be a continuous random variable with PDF 0X is a normally normally distributed variable with mean µ = 30 and standard deviation o = 4. Find a) P(x 21) c) P(30 < x < 35)If the random variable X follows the uniform distribution U= (0,1) What is the distribution of the random variable Y= -2lnX. Show its limits.If Xand Y are two gamma variates distributed as y(m)and 7(n) respectively then variable X+Y follows Chi-square distribution. Beta distribution (n +n) a) b) c) Gamma distribution with (n +m) d) Log normal distribution.X is a normally normally distributed variable with mean μ = 30 and standard deviation σ = 4. Finda) P(x < 40)b) P(x > 21)c) P(30 < x < 35)Let X,Y be i.i.d. random variables from U(0,1) distribution. (a) Give the joint distribution of X+Y and X-Y. Are they independent? Justify your answer. (b) Give the marginal distributions of X + Y and X - Y. (c) Compute E(X2 - Y).(26) Let X b(8,- Var-x) and distribution function.Let f(x, y) = x + y for 0 < x < 1 and 0 < y < 1 The Conditional Variance of Y when X = ; isSEE MORE QUESTIONS