(c) P(4< X<8) (e) Determine x such that P(X 8)
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- 6.) Suppose X is continuously uniformly distributed on [−2, 2]. Let Y = X2. What is the density function of Y? What is the expected value of Y?Suppose that two continuous random variables X and Y have a joint probability densityfunction f(x, y) = A(x − 3)y for -2≤x≤3 and 4≤y≤6a) What is the value of A?b) What is P(0≤x≤1 and 4≤y≤5)?c) Construct the marginal probability density functions.d) Are the random variables X and Y independent?e) If Y = 5, what is the conditional probability density function of X?f) What are the expectations and variances of the random variables X and Y ?g) What is the covariance of X and Y?h) What is the correlation between X and Y?a. Find the 50-th percentile of X. That is to say the value of x such that P (X ≤ x) = 0.5. b. Now say you have two independent jet engines. What is the probability that only one of themwill last more than 12 months before needing to be rebuilt? c. Find the probability density function f(x) by taking the derivative of F(x) with respect to x.
- 1) Let x be a uniform random variable in the interval (0, 1). Calculate the density function of probability of the random variable y where y = − ln x.Suppose that the joint probability density function of X and Y is fX,Y(x,y) = 10.125(x2 – y2) e−3x , for 0<x<∞ and -x<y<x 0, otherwise Give your answers to the below questions in two decimal places where appropriate. (a) The marginal probability density function of X is given by: fX(x) = A xB e-3x , for 0<x<∞ 0, otherwise Find the value of A. (b) Find the value of B. (c) The conditional probability density function of Y, given that X=x for some x>0, takes the following form: fY|X=x(y) = C (x2-y2) xD e-Ex, for -x<y<x 0, otherwise. Find the value of C (d)Find the value of D. (e)Find the value of E.Suppose that the random variable B has the standard normal density. What is the conditional probability density function of the sum of the two roots of the quadratic equation x2 + 2Bx + 1 = 0 given that the two roots are real? KINDLY REQUEST YOU TO PROVIDE ME WITH COMPLETE SOLUTION
- can you explain how you get P(X=x)xP(Y=y). is this the joint probability mass function?Find a value of k that will make f a probability density function on the indicated interval. ƒ(x) = kx; [1, 5]Find a value of k that will make f a probability density function on the indicated interval.ƒ(x) = kx; [1, 5]